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	13690k	Isogeny class
Conductor	13690	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	21888	Modular degree for the optimal curve
Δ	7594550170640 = 24 · 5 · 377	Discriminant
Eigenvalues	2-  0 5-  0 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-7102,190141]	[a1,a2,a3,a4,a6]
Generators	[343225:3112383:15625]	Generators of the group modulo torsion
j	15438249/2960	j-invariant
L	7.0587633817288	L(r)(E,1)/r!
Ω	0.70413845132346	Real period
R	10.02468103888	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	109520s1 123210x1 68450a1 370a1	Quadratic twists by: -4 -3 5 37

Hecke Eigenvalues for elliptic curve 13690k1

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	-	0	-4	-2	2	4	0	6	4	+	-6	-4	-8	10	-4	-10	-8	0	10	4	0	-2	-6

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Quadratic twists for elliptic curve 13690k1

-4	-3	5	37
109520s1	123210x1	68450a1	370a1

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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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