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	12880u	Isogeny class
Conductor	12880	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-450800 = -1 · 24 · 52 · 72 · 23	Discriminant
Eigenvalues	2-  3 5+ 7-  6 -5 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-13,-37]	[a1,a2,a3,a4,a6]
j	-15185664/28175	j-invariant
L	4.738131318049	L(r)(E,1)/r!
Ω	1.1845328295122	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3220a1 51520cn1 115920ez1 64400bg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12880u1

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
-	3	+	-	6	-5	-2	2	-	1	9	-12	1	-2	7	-4	12	8	12	-1	-7	-2	10	-6	2

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Quadratic twists for elliptic curve 12880u1

-4	8	-3	5	-7
3220a1	51520cn1	115920ez1	64400bg1	90160dk1

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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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