Atkin-Lehner |
2+ 5- 7- |
Signs for the Atkin-Lehner involutions |
Class |
78400ef |
Isogeny class |
Conductor |
78400 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-329417200000000 = -1 · 210 · 58 · 77 |
Discriminant |
Eigenvalues |
2+ 0 5- 7- 5 6 4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-24500,-1715000] |
[a1,a2,a3,a4,a6] |
Generators |
[189:637:1] |
Generators of the group modulo torsion |
j |
-34560/7 |
j-invariant |
L |
7.273404300949 |
L(r)(E,1)/r! |
Ω |
0.18874276551382 |
Real period |
R |
3.2113391116524 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002361 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78400ke1 4900r1 78400z1 11200bc1 |
Quadratic twists by: -4 8 5 -7 |