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	12880p	Isogeny class
Conductor	12880	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	807833600 = 212 · 52 · 73 · 23	Discriminant
Eigenvalues	2-  0 5+ 7- -2  4 -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2603,51098]	[a1,a2,a3,a4,a6]
Generators	[-11:280:1]	Generators of the group modulo torsion
j	476196576129/197225	j-invariant
L	4.2550192523042	L(r)(E,1)/r!
Ω	1.5634406877844	Real period
R	0.45359563744566	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	805b1 51520ce1 115920fc1 64400bi1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12880p1

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

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Quadratic twists for elliptic curve 12880p1

-4	8	-3	5	-7
805b1	51520ce1	115920fc1	64400bi1	90160co1

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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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