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	15680cd	Isogeny class
Conductor	15680	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-392000 = -1 · 26 · 53 · 72	Discriminant
Eigenvalues	2-  1 5+ 7- -2  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-16,34]	[a1,a2,a3,a4,a6]
Generators	[-3:8:1]	Generators of the group modulo torsion
j	-153664/125	j-invariant
L	5.1344429233922	L(r)(E,1)/r!
Ω	2.7528916303457	Real period
R	1.8651089882341	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	15680cj1 7840m1 78400hu1 15680dc1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15680cd1

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 15680cd1

-4	8	5	-7
15680cj1	7840m1	78400hu1	15680dc1

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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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