Atkin-Lehner |
2+ 3+ 29+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
32712a |
Isogeny class |
Conductor |
32712 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
72320 |
Modular degree for the optimal curve |
Δ |
-61295663950848 = -1 · 210 · 32 · 29 · 475 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -1 -3 -4 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,8592,-221796] |
[a1,a2,a3,a4,a6] |
Generators |
[26:136:1] [90:1128:1] |
Generators of the group modulo torsion |
j |
68494549437500/59859046827 |
j-invariant |
L |
7.1746109182925 |
L(r)(E,1)/r! |
Ω |
0.34299306576583 |
Real period |
R |
1.0458827939091 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
65424c1 98136h1 |
Quadratic twists by: -4 -3 |