Cremona's table of elliptic curves

13685 = 5 · 7 · 17 · 23

Field	Data	Notes
Atkin-Lehner	5+ 7+ 17- 23-	Signs for the Atkin-Lehner involutions
Class	13685c	Isogeny class
Conductor	13685	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	4760532046025 = 52 · 73 · 176 · 23	Discriminant
Eigenvalues	-1  0 5+ 7+  2  4 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-8353,-272344]	[a1,a2,a3,a4,a6]
Generators	[-48:151:1]	Generators of the group modulo torsion
j	64446956450965089/4760532046025	j-invariant
L	2.5649477532125	L(r)(E,1)/r!
Ω	0.50172381661217	Real period
R	1.7040900911926	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	123165h1 68425c1 95795p1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 13685c1

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

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Quadratic twists for elliptic curve 13685c1

-3	5	-7
123165h1	68425c1	95795p1

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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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