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	15680cr	Isogeny class
Conductor	15680	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	-2961967666954240 = -1 · 221 · 5 · 710	Discriminant
Eigenvalues	2-  2 5+ 7-  3  5 -6  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3201,-2618335]	[a1,a2,a3,a4,a6]
Generators	[61301:15177408:1]	Generators of the group modulo torsion
j	-49/40	j-invariant
L	6.8514766144867	L(r)(E,1)/r!
Ω	0.20329215791018	Real period
R	8.4256528693965	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15680u1 3920bg1 78400iq1 15680df1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15680cr1

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	+	-	3	5	-6	1	-3	6	-4	-11	-3	-10	3	-3	0	-4	-4	-12	4	10	12	-6	-14

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Quadratic twists for elliptic curve 15680cr1

-4	8	5	-7
15680u1	3920bg1	78400iq1	15680df1

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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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