Cremona's table of elliptic curves

Curve 58089b1

58089 = 3 · 172 · 67



Data for elliptic curve 58089b1

Field Data Notes
Atkin-Lehner 3+ 17+ 67- Signs for the Atkin-Lehner involutions
Class 58089b Isogeny class
Conductor 58089 Conductor
∏ cp 2 Product of Tamagawa factors cp
deg 55296 Modular degree for the optimal curve
Δ -43664862321 = -1 · 33 · 176 · 67 Discriminant
Eigenvalues -1 3+  1  5  4 -4 17+ -2 Hecke eigenvalues for primes up to 20
Equation [1,1,1,-295,10118] [a1,a2,a3,a4,a6]
j -117649/1809 j-invariant
L 1.9272266338993 L(r)(E,1)/r!
Ω 0.96361331752067 Real period
R 1 Regulator
r 0 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 201b1 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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