Atkin-Lehner |
2+ 3+ 11- 13+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
31746g |
Isogeny class |
Conductor |
31746 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12160 |
Modular degree for the optimal curve |
Δ |
-56380896 = -1 · 25 · 32 · 11 · 13 · 372 |
Discriminant |
Eigenvalues |
2+ 3+ -3 -1 11- 13+ 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,71,-251] |
[a1,a2,a3,a4,a6] |
Generators |
[13:-62:1] [30:59:8] |
Generators of the group modulo torsion |
j |
38717382887/56380896 |
j-invariant |
L |
4.5565814804326 |
L(r)(E,1)/r! |
Ω |
1.0523222057703 |
Real period |
R |
1.082506255082 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
95238ca1 |
Quadratic twists by: -3 |