Cremona's table of elliptic curves

1157 = 13 · 89

Field	Data	Notes
Atkin-Lehner	13- 89+	Signs for the Atkin-Lehner involutions
Class	1157c	Isogeny class
Conductor	1157	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	204	Modular degree for the optimal curve
Δ	195533 = 133 · 89	Discriminant
Eigenvalues	2  2  2 -1  4 13-  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-52,-127]	[a1,a2,a3,a4,a6]
j	15851081728/195533	j-invariant
L	5.3290548146329	L(r)(E,1)/r!
Ω	1.7763516048776	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	18512i1 74048a1 10413k1 28925a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1157c1

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
2	2	2	-1	4	-	3	-5	-2	6	0	-2	-9	2	12	3	7	0	-12	2	-8	-3	9	+	-12

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Quadratic twists for elliptic curve 1157c1

-4	8	-3	5	-7	13	89
18512i1	74048a1	10413k1	28925a1	56693b1	15041g1	102973a1

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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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