Cremona's table of elliptic curves

Curve 113715n1

113715 = 32 · 5 · 7 · 192



Data for elliptic curve 113715n1

Field Data Notes
Atkin-Lehner 3- 5+ 7+ 19- Signs for the Atkin-Lehner involutions
Class 113715n Isogeny class
Conductor 113715 Conductor
∏ cp 8 Product of Tamagawa factors cp
deg 2027520 Modular degree for the optimal curve
Δ -5345422832949609375 = -1 · 37 · 58 · 7 · 197 Discriminant
Eigenvalues -1 3- 5+ 7+ -4  2 -2 19- Hecke eigenvalues for primes up to 20
Equation [1,-1,1,-649868,230453606] [a1,a2,a3,a4,a6]
Generators [21360:381494:27] Generators of the group modulo torsion
j -885012508801/155859375 j-invariant
L 2.6806793788577 L(r)(E,1)/r!
Ω 0.23227758275878 Real period
R 5.7704220238254 Regulator
r 1 Rank of the group of rational points
S 1.0000000076374 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 37905t1 5985h1 Quadratic twists by: -3 -19


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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