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	12880n	Isogeny class
Conductor	12880	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-10196798832640 = -1 · 215 · 5 · 76 · 232	Discriminant
Eigenvalues	2-  2 5+ 7+  0  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,784,-153664]	[a1,a2,a3,a4,a6]
Generators	[97722:1115686:729]	Generators of the group modulo torsion
j	12994449551/2489452840	j-invariant
L	6.0292449201962	L(r)(E,1)/r!
Ω	0.34116346335823	Real period
R	8.8362992637716	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	1610d2 51520cc2 115920dx2 64400bt2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12880n2

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	+	+	0	2	-6	4	-	6	-2	-10	-6	10	0	6	12	-10	-2	-12	-16	10	12	-6	-10

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Quadratic twists for elliptic curve 12880n2

-4	8	-3	5	-7
1610d2	51520cc2	115920dx2	64400bt2	90160dg2

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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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