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	15680cp	Isogeny class
Conductor	15680	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-30118144000000 = -1 · 214 · 56 · 76	Discriminant
Eigenvalues	2-  2 5+ 7-  0  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7121,-348655]	[a1,a2,a3,a4,a6]
Generators	[3145:176280:1]	Generators of the group modulo torsion
j	-20720464/15625	j-invariant
L	6.7269608230818	L(r)(E,1)/r!
Ω	0.25161533602219	Real period
R	6.6837746552227	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	15680s4 3920bf4 78400ik4 320f4	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15680cp4

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

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Quadratic twists for elliptic curve 15680cp4

-4	8	5	-7
15680s4	3920bf4	78400ik4	320f4

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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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