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	12880w	Isogeny class
Conductor	12880	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	107520	Modular degree for the optimal curve
Δ	16213543485440000 = 226 · 54 · 75 · 23	Discriminant
Eigenvalues	2-  2 5- 7+  2 -4 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-145920,-20512768]	[a1,a2,a3,a4,a6]
Generators	[1922:82434:1]	Generators of the group modulo torsion
j	83890194895342081/3958384640000	j-invariant
L	6.8357075244497	L(r)(E,1)/r!
Ω	0.24498449955569	Real period
R	6.975653089121	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	1610g1 51520bn1 115920dd1 64400bz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12880w1

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	-	+	2	-4	-2	4	+	-2	4	-8	-2	-10	12	-4	-10	-14	-10	16	6	4	-12	-6	-14

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Quadratic twists for elliptic curve 12880w1

-4	8	-3	5	-7
1610g1	51520bn1	115920dd1	64400bz1	90160bw1

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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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