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	15680di	Isogeny class
Conductor	15680	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	555600341277900800 = 215 · 52 · 714	Discriminant
Eigenvalues	2-  0 5- 7-  0 -2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-209132,8303344]	[a1,a2,a3,a4,a6]
j	262389836808/144120025	j-invariant
L	2.0283940862753	L(r)(E,1)/r!
Ω	0.25354926078442	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15680dj4 7840q2 78400gp3 2240t4	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15680di3

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
-	0	-	-	0	-2	-2	8	8	-6	0	2	6	-8	8	2	8	-2	-8	0	-10	-16	16	-10	14

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Quadratic twists for elliptic curve 15680di3

-4	8	5	-7
15680dj4	7840q2	78400gp3	2240t4

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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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