Cremona's table of elliptic curves

Curve 89b2

89 = Prime conductor



Data for elliptic curve 89b2

Field Data Notes
Atkin-Lehner 89- Signs for the Atkin-Lehner involutions
Class 89b Isogeny class
Conductor 89 Conductor
∏ cp 1 Product of Tamagawa factors cp
Δ 89 = Prime discriminant Discriminant
Eigenvalues  1  2 -2  2 -4  2  6 -2 Hecke eigenvalues for primes up to 20
Equation [1,1,0,-1,0] [a1,a2,a3,a4,a6]
j 389017/89 j-invariant
L 1.4223048292271 L(r)(E,1)/r!
Ω 5.6892193169084 Real period
R 1 Regulator
r 0 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 1424f1 5696g1 801b1 2225b1 Quadratic twists by: -4 8 -3 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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