Cremona's table of elliptic curves

1157 = 13 · 89

Field	Data	Notes
Atkin-Lehner	13+ 89+	Signs for the Atkin-Lehner involutions
Class	1157a	Isogeny class
Conductor	1157	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	36	Modular degree for the optimal curve
Δ	1157 = 13 · 89	Discriminant
Eigenvalues	0 -2  0  1  2 13+ -1  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-3,-3]	[a1,a2,a3,a4,a6]
Generators	[-1:0:1]	Generators of the group modulo torsion
j	4096000/1157	j-invariant
L	1.6643817710831	L(r)(E,1)/r!
Ω	3.6089997513227	Real period
R	0.46117536319393	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	18512f1 74048h1 10413f1 28925b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1157a1

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
0	-2	0	1	2	+	-1	5	-4	6	4	-6	5	-10	-8	-5	-7	-10	8	-2	10	-11	-17	+	8

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Quadratic twists for elliptic curve 1157a1

-4	8	-3	5	-7	13	89
18512f1	74048h1	10413f1	28925b1	56693c1	15041c1	102973c1

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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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