Atkin-Lehner |
2+ 3+ 5- 13- 31- |
Signs for the Atkin-Lehner involutions |
Class |
36270h |
Isogeny class |
Conductor |
36270 |
Conductor |
∏ cp |
324 |
Product of Tamagawa factors cp |
deg |
466560 |
Modular degree for the optimal curve |
Δ |
-13806033820312500 = -1 · 22 · 33 · 59 · 133 · 313 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -4 -3 13- 0 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-239754,45597528] |
[a1,a2,a3,a4,a6] |
Generators |
[-558:2604:1] [279:-744:1] |
Generators of the group modulo torsion |
j |
-56449298801755712763/511334585937500 |
j-invariant |
L |
6.3182315849636 |
L(r)(E,1)/r! |
Ω |
0.3987444287603 |
Real period |
R |
0.44014767419154 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999985 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
36270bf2 |
Quadratic twists by: -3 |