Cremona's table of elliptic curves

Curve 338a1

338 = 2 · 132



Data for elliptic curve 338a1

Field Data Notes
Atkin-Lehner 2+ 13+ Signs for the Atkin-Lehner involutions
Class 338a Isogeny class
Conductor 338 Conductor
∏ cp 2 Product of Tamagawa factors cp
deg 12 Modular degree for the optimal curve
Δ -676 = -1 · 22 · 132 Discriminant
Eigenvalues 2+  0  1 -4 -4 13+  3  0 Hecke eigenvalues for primes up to 20
Equation [1,-1,0,1,1] [a1,a2,a3,a4,a6]
Generators [0:1:1] Generators of the group modulo torsion
j 351/4 j-invariant
L 1.2776773619189 L(r)(E,1)/r!
Ω 3.7619828721783 Real period
R 0.16981435127841 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 2704d1 10816b1 3042l1 8450o1 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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