Cremona's table of elliptic curves

Curve 31977a2

31977 = 32 · 11 · 17 · 19



Data for elliptic curve 31977a2

Field Data Notes
Atkin-Lehner 3+ 11+ 17+ 19+ Signs for the Atkin-Lehner involutions
Class 31977a Isogeny class
Conductor 31977 Conductor
∏ cp 8 Product of Tamagawa factors cp
Δ -687629328538158171 = -1 · 39 · 112 · 17 · 198 Discriminant
Eigenvalues  1 3+ -2 -2 11+ -2 17+ 19+ Hecke eigenvalues for primes up to 20
Equation [1,-1,0,-803913,-280088380] [a1,a2,a3,a4,a6]
Generators [99511314263298158:-30910303914554035817:1034591361544] Generators of the group modulo torsion
j -2919173302382502339/34935189175337 j-invariant
L 3.8292297985151 L(r)(E,1)/r!
Ω 0.079663202558337 Real period
R 24.033868056654 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 31977e2 Quadratic twists by: -3


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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