Cremona's table of elliptic curves

Curve 113475m1

113475 = 3 · 52 · 17 · 89



Data for elliptic curve 113475m1

Field Data Notes
Atkin-Lehner 3- 5+ 17+ 89- Signs for the Atkin-Lehner involutions
Class 113475m Isogeny class
Conductor 113475 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 112896 Modular degree for the optimal curve
Δ -30141796875 = -1 · 3 · 58 · 172 · 89 Discriminant
Eigenvalues -2 3- 5+  0  4  0 17+  2 Hecke eigenvalues for primes up to 20
Equation [0,1,1,-8,-8356] [a1,a2,a3,a4,a6]
Generators [24:76:1] Generators of the group modulo torsion
j -4096/1929075 j-invariant
L 4.8323074200388 L(r)(E,1)/r!
Ω 0.5380498863273 Real period
R 2.2452878027761 Regulator
r 1 Rank of the group of rational points
S 1.000000006584 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 22695c1 Quadratic twists by: 5


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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