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	15680cz	Isogeny class
Conductor	15680	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-46118408000 = -1 · 26 · 53 · 78	Discriminant
Eigenvalues	2-  1 5- 7+  2 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-800,13250]	[a1,a2,a3,a4,a6]
Generators	[65:490:1]	Generators of the group modulo torsion
j	-153664/125	j-invariant
L	6.0501586332186	L(r)(E,1)/r!
Ω	1.0404952343151	Real period
R	0.64607681608256	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	15680dc1 7840b1 78400gd1 15680cj1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15680cz1

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	-	+	2	-2	-2	0	1	1	-2	-4	5	-11	8	8	4	5	1	-12	6	4	-13	-3	-2

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Quadratic twists for elliptic curve 15680cz1

-4	8	5	-7
15680dc1	7840b1	78400gd1	15680cj1

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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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