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	12640b	Isogeny class
Conductor	12640	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2176	Modular degree for the optimal curve
Δ	-1617920 = -1 · 212 · 5 · 79	Discriminant
Eigenvalues	2+ -1 5+ -5 -3  0  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,19,-59]	[a1,a2,a3,a4,a6]
Generators	[3:4:1]	Generators of the group modulo torsion
j	175616/395	j-invariant
L	2.1458700095284	L(r)(E,1)/r!
Ω	1.3834945189358	Real period
R	0.77552530210923	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	12640c1 25280y1 113760bl1 63200n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12640b1

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	+	-5	-3	0	6	-4	-6	-6	3	7	2	12	-8	-3	8	10	-8	-2	0	+	0	10	-2

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Quadratic twists for elliptic curve 12640b1

-4	8	-3	5
12640c1	25280y1	113760bl1	63200n1

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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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