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	13690b	Isogeny class
Conductor	13690	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	10396939183606160 = 24 · 5 · 379	Discriminant
Eigenvalues	2+ -2 5+  2  0 -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-7221504,-7470066178]	[a1,a2,a3,a4,a6]
Generators	[584840117184477:-44514759626286349:84546715869]	Generators of the group modulo torsion
j	16232905099479601/4052240	j-invariant
L	1.9813444486104	L(r)(E,1)/r!
Ω	0.092096400035449	Real period
R	21.513809962689	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	109520k3 123210dj3 68450y3 370d3	Quadratic twists by: -4 -3 5 37

Hecke Eigenvalues for elliptic curve 13690b3

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

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Quadratic twists for elliptic curve 13690b3

-4	-3	5	37
109520k3	123210dj3	68450y3	370d3

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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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