Atkin-Lehner |
3- 37+ 73+ |
Signs for the Atkin-Lehner involutions |
Class |
24309b |
Isogeny class |
Conductor |
24309 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
21504 |
Modular degree for the optimal curve |
Δ |
53110619217 = 312 · 372 · 73 |
Discriminant |
Eigenvalues |
-1 3- -2 -2 0 4 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-3011,63362] |
[a1,a2,a3,a4,a6] |
Generators |
[-26:364:1] [-15:331:1] |
Generators of the group modulo torsion |
j |
4139932137193/72854073 |
j-invariant |
L |
4.5404252507427 |
L(r)(E,1)/r! |
Ω |
1.1228339441772 |
Real period |
R |
2.0218596321782 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8103d1 |
Quadratic twists by: -3 |