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
deg	23040	Modular degree for the optimal curve
Δ	-9828911411200 = -1 · 212 · 52 · 73 · 234	Discriminant
Eigenvalues	2-  0 5+ 7-  4 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,37,-150838]	[a1,a2,a3,a4,a6]
Generators	[61:280:1]	Generators of the group modulo torsion
j	1367631/2399636575	j-invariant
L	4.4470206244001	L(r)(E,1)/r!
Ω	0.33331955885797	Real period
R	1.1118010995306	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	805c1 51520cg1 115920fi1 64400bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12880q1

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 12880q1

-4	8	-3	5	-7
805c1	51520cg1	115920fi1	64400bj1	90160cp1

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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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