Atkin-Lehner |
3+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
12321a |
Isogeny class |
Conductor |
12321 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
21888 |
Modular degree for the optimal curve |
Δ |
-2563160682591 = -1 · 33 · 377 |
Discriminant |
Eigenvalues |
1 3+ -2 -4 -4 2 -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,1797,-71680] |
[a1,a2,a3,a4,a6] |
Generators |
[14336:86848:343] |
Generators of the group modulo torsion |
j |
9261/37 |
j-invariant |
L |
3.382948261452 |
L(r)(E,1)/r! |
Ω |
0.41156178045418 |
Real period |
R |
8.219782356172 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
12321b1 333c1 |
Quadratic twists by: -3 37 |