Cremona's table of elliptic curves

1078 = 2 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	1078g	Isogeny class
Conductor	1078	Conductor
∏ cp	45	Product of Tamagawa factors cp
deg	1680	Modular degree for the optimal curve
Δ	2077910990848 = 215 · 78 · 11	Discriminant
Eigenvalues	2-  1  0 7+ 11+  5  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3823,-59207]	[a1,a2,a3,a4,a6]
j	1071912625/360448	j-invariant
L	3.1181180335845	L(r)(E,1)/r!
Ω	0.6236236067169	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	8624n1 34496g1 9702m1 26950c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1078g1

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	0	+	+	5	6	2	6	3	8	2	-6	-4	6	-12	-3	-7	-13	-12	-10	-1	6	6	-13

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Quadratic twists for elliptic curve 1078g1

-4	8	-3	5	-7	-11
8624n1	34496g1	9702m1	26950c1	1078j1	11858c1

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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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