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	15680bu	Isogeny class
Conductor	15680	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	1798307840000 = 223 · 54 · 73	Discriminant
Eigenvalues	2+  2 5- 7-  4  2 -8 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-76225,8125377]	[a1,a2,a3,a4,a6]
Generators	[177:384:1]	Generators of the group modulo torsion
j	544737993463/20000	j-invariant
L	7.5594361608998	L(r)(E,1)/r!
Ω	0.78289043739252	Real period
R	1.206975427187	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	15680dt2 490g2 78400cv2 15680v2	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15680bu2

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	-	-	4	2	-8	-6	-4	6	-4	10	-4	-4	-4	-10	-14	-10	4	12	-4	4	-2	-8	0

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Quadratic twists for elliptic curve 15680bu2

-4	8	5	-7
15680dt2	490g2	78400cv2	15680v2

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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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