Atkin-Lehner |
2- 3- 5- 19- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
17670z |
Isogeny class |
Conductor |
17670 |
Conductor |
∏ cp |
1536 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
-3431318484418560000 = -1 · 224 · 34 · 54 · 194 · 31 |
Discriminant |
Eigenvalues |
2- 3- 5- 0 0 -6 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-460190,149564100] |
[a1,a2,a3,a4,a6] |
Generators |
[-500:16210:1] |
Generators of the group modulo torsion |
j |
-10777928608322539918561/3431318484418560000 |
j-invariant |
L |
9.398428913781 |
L(r)(E,1)/r! |
Ω |
0.23688820874563 |
Real period |
R |
0.41327637919853 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
53010k1 88350e1 |
Quadratic twists by: -3 5 |