Atkin-Lehner |
2+ 3+ 11- 37- |
Signs for the Atkin-Lehner involutions |
Class |
78144s |
Isogeny class |
Conductor |
78144 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
5591040 |
Modular degree for the optimal curve |
Δ |
9.7923034001868E+19 |
Discriminant |
Eigenvalues |
2+ 3+ -2 2 11- 4 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-78599584,-268185552326] |
[a1,a2,a3,a4,a6] |
Generators |
[13060883003381625760653214:-174600442692069016753953075:1265916442277162552408] |
Generators of the group modulo torsion |
j |
839082157271345371360241728/1530047406279184551 |
j-invariant |
L |
4.8424082946048 |
L(r)(E,1)/r! |
Ω |
0.05070427062994 |
Real period |
R |
38.201186866991 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002856 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78144bf1 39072n2 |
Quadratic twists by: -4 8 |