Elliptic curves by rank › curves from searches
Torsion Z/4xZ/2: record curves
The curves of this collection with torsion subgroup Z/4xZ/2, by rank: for each rank the
ten smallest conductors, with generators of the Mordell-Weil group and of the torsion
subgroup. Every curve has proven rank, is given by its global minimal model, and
appears in the corresponding rank_r file as well. Conductors are exact integers;
heights are natural logarithms; the naive height is log max(abs(c4)^3, c6^2).
| rank | curves | smallest log N | smallest naive height | smallest log abs(disc) |
|---|---|---|---|---|
| 4 | 2 | 22.553340 | 79.520692 | 67.501190 |
Rank 4
| # | a-invariants | conductor N | log N | naive h | log abs(disc) | torsion generators |
|---|---|---|---|---|---|---|
| 1 | [0,-1,0,-12528422340,539310754124100] |
6234348120 |
22.553339859 | 81.367400000 | 67.50119043 | [[41820,9407970],[63105,0]] |
| 2 | [1,0,0,-6769521299,122205015087249] |
39992228166 |
24.411950976 | 79.520692000 | 71.67300828 | [[-20480,15892777],[19078,-9539]] |
generators for these ten
1. [0,-1,0,-12528422340,539310754124100] N = 6234348120
E = ellinit([0,-1,0,-12528422340,539310754124100]);
generators:
[107457,20828808]
[1191785/16,281716435/64]
[-108715,24827990]
[4118845/36,5306617745/216]
torsion generators:
[41820,9407970]
[63105,0]
2. [1,0,0,-6769521299,122205015087249] N = 39992228166
E = ellinit([1,0,0,-6769521299,122205015087249]);
generators:
[18064,2402377]
[96028,18863731]
[-373451/16,1047483901/64]
[2900806/9,4781862839/27]
torsion generators:
[-20480,15892777]
[19078,-9539]