Atkin-Lehner |
2+ 3+ 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
10998b |
Isogeny class |
Conductor |
10998 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
25344 |
Modular degree for the optimal curve |
Δ |
9329119488 = 28 · 33 · 13 · 473 |
Discriminant |
Eigenvalues |
2+ 3+ 0 2 0 13- 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-84372,9454032] |
[a1,a2,a3,a4,a6] |
Generators |
[196780920:-151308452:1157625] |
Generators of the group modulo torsion |
j |
2460128970701158875/345522944 |
j-invariant |
L |
3.6174279005037 |
L(r)(E,1)/r! |
Ω |
1.0114191092402 |
Real period |
R |
10.729759406725 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
6 |
Number of elements in the torsion subgroup |
Twists |
87984o1 10998k3 |
Quadratic twists by: -4 -3 |