Cremona's table of elliptic curves

1264 = 2⁴ · 79

Field	Data	Notes
Atkin-Lehner	2+ 79+	Signs for the Atkin-Lehner involutions
Class	1264a	Isogeny class
Conductor	1264	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	80896 = 210 · 79	Discriminant
Eigenvalues	2+ -1 -1  5 -4  1 -8 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-16,-16]	[a1,a2,a3,a4,a6]
Generators	[-2:2:1]	Generators of the group modulo torsion
j	470596/79	j-invariant
L	2.3225026130698	L(r)(E,1)/r!
Ω	2.4019398926569	Real period
R	0.48346393266751	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	632a1 5056l1 11376c1 31600b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1264a1

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	-4	1	-8	-2	6	0	4	-2	0	-8	-3	-10	-15	-4	0	-3	-14	+	-6	9	-7

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Quadratic twists for elliptic curve 1264a1

-4	8	-3	5	-7	-79
632a1	5056l1	11376c1	31600b1	61936a1	99856a1

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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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