Cremona's table of elliptic curves

12880 = 2⁴ · 5 · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 23+	Signs for the Atkin-Lehner involutions
Class	12880q	Isogeny class
Conductor	12880	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	32598999615795200 = 212 · 52 · 712 · 23	Discriminant
Eigenvalues	2-  0 5+ 7-  4 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-88283,5145418]	[a1,a2,a3,a4,a6]
Generators	[402:7315:8]	Generators of the group modulo torsion
j	18577831198352049/7958740140575	j-invariant
L	4.4470206244001	L(r)(E,1)/r!
Ω	0.33331955885797	Real period
R	4.4472043981223	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	805c3 51520cg3 115920fi3 64400bj3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12880q4

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

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Quadratic twists for elliptic curve 12880q4

-4	8	-3	5	-7
805c3	51520cg3	115920fi3	64400bj3	90160cp3

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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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