Atkin-Lehner |
3+ 7+ 11+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
12243a |
Isogeny class |
Conductor |
12243 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
-126029870773893009 = -1 · 316 · 73 · 115 · 53 |
Discriminant |
Eigenvalues |
-1 3+ 3 7+ 11+ -3 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-39914,17337224] |
[a1,a2,a3,a4,a6] |
Generators |
[5370:492608:125] |
Generators of the group modulo torsion |
j |
-7032344716371443617/126029870773893009 |
j-invariant |
L |
2.6846764604098 |
L(r)(E,1)/r! |
Ω |
0.27814160957908 |
Real period |
R |
4.8260964342455 |
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 |
36729r1 85701t1 |
Quadratic twists by: -3 -7 |