Cremona's table of elliptic curves

31117 = 29² · 37

Field	Data	Notes
Atkin-Lehner	29- 37+	Signs for the Atkin-Lehner involutions
Class	31117f	Isogeny class
Conductor	31117	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	30688	Modular degree for the optimal curve
Δ	-33388541 = -1 · 293 · 372	Discriminant
Eigenvalues	-1 -1 -3 -4 -3 -5  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-11342,460200]	[a1,a2,a3,a4,a6]
Generators	[60:-45:1] [-3:704:1]	Generators of the group modulo torsion
j	-6616084455917/1369	j-invariant
L	2.7176322085627	L(r)(E,1)/r!
Ω	1.6418232614382	Real period
R	0.41381314791808	Regulator
r	2	Rank of the group of rational points
S	0.99999999999974	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	31117g1	Quadratic twists by: 29

Hecke Eigenvalues for elliptic curve 31117f1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-1	-1	-3	-4	-3	-5	4	0	0	-	1	+	-4	-1	-9	-1	10	-10	10	-2	14	-5	-6	12	-16

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Quadratic twists for elliptic curve 31117f1

29
31117g1

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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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