Cremona's table of elliptic curves

3157 = 7 · 11 · 41

Field	Data	Notes
Atkin-Lehner	7+ 11- 41-	Signs for the Atkin-Lehner involutions
Class	3157a	Isogeny class
Conductor	3157	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-3157 = -1 · 7 · 11 · 41	Discriminant
Eigenvalues	1 -2  0 7+ 11-  2  2  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1,-3]	[a1,a2,a3,a4,a6]
Generators	[3:3:1]	Generators of the group modulo torsion
j	-15625/3157	j-invariant
L	2.7962622802528	L(r)(E,1)/r!
Ω	2.0010523071801	Real period
R	1.3973958952594	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	50512k1 28413c1 78925h1 22099c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3157a1

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	-2	0	+	-	2	2	1	6	9	-7	-11	-	-1	-6	12	12	-5	-9	-3	-13	-14	-4	-7	13

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Quadratic twists for elliptic curve 3157a1

-4	-3	5	-7	-11	41
50512k1	28413c1	78925h1	22099c1	34727a1	129437c1

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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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