Atkin-Lehner |
2+ 3- 5+ 13- 103- |
Signs for the Atkin-Lehner involutions |
Class |
40170j |
Isogeny class |
Conductor |
40170 |
Conductor |
∏ cp |
180 |
Product of Tamagawa factors cp |
deg |
362880 |
Modular degree for the optimal curve |
Δ |
-5195245622299200 = -1 · 26 · 315 · 52 · 133 · 103 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -1 -3 13- 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-139144,20264726] |
[a1,a2,a3,a4,a6] |
Generators |
[-431:683:1] [-332:5633:1] |
Generators of the group modulo torsion |
j |
-297928930275221509369/5195245622299200 |
j-invariant |
L |
7.4419912253768 |
L(r)(E,1)/r! |
Ω |
0.43112099398367 |
Real period |
R |
0.86309775320961 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
120510bi1 |
Quadratic twists by: -3 |