Cremona's table of elliptic curves

Curve 71672a1

71672 = 23 · 172 · 31



Data for elliptic curve 71672a1

Field Data Notes
Atkin-Lehner 2+ 17+ 31+ Signs for the Atkin-Lehner involutions
Class 71672a Isogeny class
Conductor 71672 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 82944 Modular degree for the optimal curve
Δ -3459975690736 = -1 · 24 · 178 · 31 Discriminant
Eigenvalues 2+  0 -3  1  0 -4 17+ -3 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-3179,112999] [a1,a2,a3,a4,a6]
Generators [51:289:1] Generators of the group modulo torsion
j -9199872/8959 j-invariant
L 3.2602640970724 L(r)(E,1)/r!
Ω 0.72172597792777 Real period
R 1.1293289271245 Regulator
r 1 Rank of the group of rational points
S 0.99999999992278 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 4216c1 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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