Atkin-Lehner |
2+ 3- 5- 13+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69030s |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
875520 |
Modular degree for the optimal curve |
Δ |
-1465759825920 = -1 · 219 · 36 · 5 · 13 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 5- -4 0 13+ -4 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1347264,-601567232] |
[a1,a2,a3,a4,a6] |
Generators |
[1984717394667577890343968467738484735:205049280696579339365555309373731372266:181972317266530678915014530394125] |
Generators of the group modulo torsion |
j |
-370983403154885372929/2010644480 |
j-invariant |
L |
4.12531432546 |
L(r)(E,1)/r! |
Ω |
0.070065845556836 |
Real period |
R |
58.877678456241 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7670f1 |
Quadratic twists by: -3 |