Cremona's table of elliptic curves

1131 = 3 · 13 · 29

Field	Data	Notes
Atkin-Lehner	3+ 13+ 29+	Signs for the Atkin-Lehner involutions
Class	1131a	Isogeny class
Conductor	1131	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-132327 = -1 · 33 · 132 · 29	Discriminant
Eigenvalues	-1 3+  0  0 -4 13+  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,12,12]	[a1,a2,a3,a4,a6]
Generators	[0:3:1]	Generators of the group modulo torsion
j	190109375/132327	j-invariant
L	1.4370880197726	L(r)(E,1)/r!
Ω	2.0784572938202	Real period
R	1.3828410369994	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	18096ba1 72384bi1 3393e1 28275g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1131a1

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	+	0	0	-4	+	6	2	0	+	10	-8	2	0	4	-2	6	-10	-8	-2	-12	-16	-14	6	-12

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Quadratic twists for elliptic curve 1131a1

-4	8	-3	5	-7	13	29
18096ba1	72384bi1	3393e1	28275g1	55419h1	14703a1	32799f1

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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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