Cremona's table of elliptic curves

1264 = 2⁴ · 79

Field	Data	Notes
Atkin-Lehner	2- 79+	Signs for the Atkin-Lehner involutions
Class	1264b	Isogeny class
Conductor	1264	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	1294336 = 214 · 79	Discriminant
Eigenvalues	2- -1  3  1  0  5  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-744,-7568]	[a1,a2,a3,a4,a6]
j	11134383337/316	j-invariant
L	1.8280514842269	L(r)(E,1)/r!
Ω	0.91402574211344	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	158d3 5056n1 11376n1 31600g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1264b1

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	3	1	0	5	0	-2	6	0	4	2	-12	-8	9	6	9	8	4	9	2	+	-18	9	17

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Quadratic twists for elliptic curve 1264b1

-4	8	-3	5	-7	-79
158d3	5056n1	11376n1	31600g1	61936n1	99856g1

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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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