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	12880v	Isogeny class
Conductor	12880	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	107520	Modular degree for the optimal curve
Δ	-96585372143750000 = -1 · 24 · 58 · 74 · 235	Discriminant
Eigenvalues	2- -1 5- 7+  2 -1 -8 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,102230,-8114725]	[a1,a2,a3,a4,a6]
Generators	[265:6125:1]	Generators of the group modulo torsion
j	7384729019637956864/6036585758984375	j-invariant
L	3.6655228430987	L(r)(E,1)/r!
Ω	0.18693722197157	Real period
R	1.2255193228907	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	3220d1 51520bk1 115920db1 64400bw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12880v1

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

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Quadratic twists for elliptic curve 12880v1

-4	8	-3	5	-7
3220d1	51520bk1	115920db1	64400bw1	90160bt1

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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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