Atkin-Lehner |
2+ 3+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
89304g |
Isogeny class |
Conductor |
89304 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
70560 |
Modular degree for the optimal curve |
Δ |
-2083283712 = -1 · 28 · 37 · 612 |
Discriminant |
Eigenvalues |
2+ 3+ 4 0 -6 1 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-81,-2187] |
[a1,a2,a3,a4,a6] |
Generators |
[37:210:1] |
Generators of the group modulo torsion |
j |
-62464/2187 |
j-invariant |
L |
7.5686861927591 |
L(r)(E,1)/r! |
Ω |
0.64035203918144 |
Real period |
R |
2.9548926654337 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000022815 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89304k1 |
Quadratic twists by: 61 |