Cremona's table of elliptic curves

15680 = 2⁶ · 5 · 7²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7-	Signs for the Atkin-Lehner involutions
Class	15680x	Isogeny class
Conductor	15680	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-561971200 = -1 · 216 · 52 · 73	Discriminant
Eigenvalues	2+ -2 5+ 7- -4 -2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,159,895]	[a1,a2,a3,a4,a6]
Generators	[-3:20:1] [2:35:1]	Generators of the group modulo torsion
j	19652/25	j-invariant
L	4.7726039404358	L(r)(E,1)/r!
Ω	1.1003982331632	Real period
R	1.084290168005	Regulator
r	2	Rank of the group of rational points
S	0.99999999999995	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15680cs1 1960o1 78400cn1 15680bv1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15680x1

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	+	-	-4	-2	0	-2	-4	-10	4	2	-12	4	4	-2	-10	-6	-4	-12	-4	-4	-14	8	-8

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Quadratic twists for elliptic curve 15680x1

-4	8	5	-7
15680cs1	1960o1	78400cn1	15680bv1

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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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