Cremona's table of elliptic curves

12640 = 2⁵ · 5 · 79

Field	Data	Notes
Atkin-Lehner	2+ 5+ 79+	Signs for the Atkin-Lehner involutions
Class	12640a	Isogeny class
Conductor	12640	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	47232	Modular degree for the optimal curve
Δ	-10097438720 = -1 · 212 · 5 · 793	Discriminant
Eigenvalues	2+  1 5+  1  5  0  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-572221,166416619]	[a1,a2,a3,a4,a6]
Generators	[477:1492:1]	Generators of the group modulo torsion
j	-5058897720777362944/2465195	j-invariant
L	5.4864621597612	L(r)(E,1)/r!
Ω	0.78321354272638	Real period
R	3.5025327451967	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	12640d1 25280j1 113760bg1 63200o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12640a1

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	0	2	-4	-6	-2	7	5	-10	4	-8	-1	0	2	-12	6	4	+	-16	-6	-2

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Quadratic twists for elliptic curve 12640a1

-4	8	-3	5
12640d1	25280j1	113760bg1	63200o1

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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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