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	12880g	Isogeny class
Conductor	12880	Conductor
∏ cp	50	Product of Tamagawa factors cp
deg	144000	Modular degree for the optimal curve
Δ	-7112722400000 = -1 · 28 · 55 · 75 · 232	Discriminant
Eigenvalues	2+  1 5- 7- -1  5 -7  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2071545,1146907475]	[a1,a2,a3,a4,a6]
Generators	[910:4025:1]	Generators of the group modulo torsion
j	-3840316976122235063296/27784071875	j-invariant
L	6.0340958805509	L(r)(E,1)/r!
Ω	0.51377056880995	Real period
R	0.23489457150213	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	6440i1 51520bq1 115920y1 64400h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12880g1

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	-	-	-1	5	-7	4	+	-9	-6	-4	8	2	5	6	-6	10	-16	0	-10	1	4	-18	5

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Quadratic twists for elliptic curve 12880g1

-4	8	-3	5	-7
6440i1	51520bq1	115920y1	64400h1	90160e1

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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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