Atkin-Lehner |
2- 3+ 5+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
68400do |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
1105920 |
Modular degree for the optimal curve |
Δ |
612723916800000000 = 222 · 39 · 58 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -4 -6 0 4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-222075,-14289750] |
[a1,a2,a3,a4,a6] |
Generators |
[-410:2800:1] |
Generators of the group modulo torsion |
j |
961504803/486400 |
j-invariant |
L |
4.4101226009495 |
L(r)(E,1)/r! |
Ω |
0.2319780403607 |
Real period |
R |
4.7527371492193 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000109 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8550t1 68400dn1 13680w1 |
Quadratic twists by: -4 -3 5 |