Cremona's table of elliptic curves

13690 = 2 · 5 · 37²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 37+	Signs for the Atkin-Lehner involutions
Class	13690a	Isogeny class
Conductor	13690	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	31968	Modular degree for the optimal curve
Δ	35124794539210 = 2 · 5 · 378	Discriminant
Eigenvalues	2+  1 5+  2  0  5  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-13719,547656]	[a1,a2,a3,a4,a6]
Generators	[-185552635344:-10366664746019:12024728171]	Generators of the group modulo torsion
j	81289/10	j-invariant
L	4.2711632713966	L(r)(E,1)/r!
Ω	0.6301489685086	Real period
R	20.33406456971	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	109520j1 123210dk1 68450x1 13690l1	Quadratic twists by: -4 -3 5 37

Hecke Eigenvalues for elliptic curve 13690a1

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	5	0	2	0	6	-1	+	-9	-1	-6	-9	-12	-10	-4	-12	8	-4	-12	6	2

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Quadratic twists for elliptic curve 13690a1

-4	-3	5	37
109520j1	123210dk1	68450x1	13690l1

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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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