Cremona's table of elliptic curves

Curve 47974b1

47974 = 2 · 172 · 83



Data for elliptic curve 47974b1

Field Data Notes
Atkin-Lehner 2+ 17+ 83+ Signs for the Atkin-Lehner involutions
Class 47974b Isogeny class
Conductor 47974 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 69120 Modular degree for the optimal curve
Δ -68116219718 = -1 · 2 · 177 · 83 Discriminant
Eigenvalues 2+  1 -4  0 -3  5 17+  5 Hecke eigenvalues for primes up to 20
Equation [1,0,1,-1018,-17798] [a1,a2,a3,a4,a6]
Generators [430:2093:8] Generators of the group modulo torsion
j -4826809/2822 j-invariant
L 3.5324240709068 L(r)(E,1)/r!
Ω 0.41159007769173 Real period
R 2.145595983963 Regulator
r 1 Rank of the group of rational points
S 0.99999999999131 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 2822b1 Quadratic twists by: 17


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

Part of Computational Number Theory
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