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	15680bh	Isogeny class
Conductor	15680	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	-4917248000 = -1 · 214 · 53 · 74	Discriminant
Eigenvalues	2+ -1 5- 7+ -6 -2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3985,98225]	[a1,a2,a3,a4,a6]
Generators	[355:-6580:1] [-35:440:1]	Generators of the group modulo torsion
j	-177953104/125	j-invariant
L	5.941758596687	L(r)(E,1)/r!
Ω	1.3549764945001	Real period
R	0.12180938236045	Regulator
r	2	Rank of the group of rational points
S	0.99999999999993	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15680da1 980a1 78400e1 15680n1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15680bh1

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	-	+	-6	-2	-6	-8	3	-3	2	-8	-3	-5	0	-12	0	1	7	0	-10	-4	-3	-3	-10

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Quadratic twists for elliptic curve 15680bh1

-4	8	5	-7
15680da1	980a1	78400e1	15680n1

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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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