Cremona's table of elliptic curves

Curve 61488q1

61488 = 24 · 32 · 7 · 61



Data for elliptic curve 61488q1

Field Data Notes
Atkin-Lehner 2- 3+ 7- 61+ Signs for the Atkin-Lehner involutions
Class 61488q Isogeny class
Conductor 61488 Conductor
∏ cp 24 Product of Tamagawa factors cp
deg 262656 Modular degree for the optimal curve
Δ 26989521076224 = 216 · 39 · 73 · 61 Discriminant
Eigenvalues 2- 3+ -2 7-  0  6  0  0 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-187731,31306770] [a1,a2,a3,a4,a6]
Generators [222:756:1] Generators of the group modulo torsion
j 9075706699779/334768 j-invariant
L 6.2068750472498 L(r)(E,1)/r!
Ω 0.62477515429808 Real period
R 1.6557623449183 Regulator
r 1 Rank of the group of rational points
S 1.0000000000139 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 7686a1 61488p1 Quadratic twists by: -4 -3


Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations