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	1078f	Isogeny class
Conductor	1078	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-1594379248 = -1 · 24 · 77 · 112	Discriminant
Eigenvalues	2+ -2 -2 7- 11-  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-712,7494]	[a1,a2,a3,a4,a6]
Generators	[-3:99:1]	Generators of the group modulo torsion
j	-338608873/13552	j-invariant
L	1.2712659146348	L(r)(E,1)/r!
Ω	1.4905278275133	Real period
R	0.21322411617697	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8624u1 34496u1 9702bw1 26950cv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1078f1

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
+	-2	-2	-	-	4	0	-4	4	2	10	-6	0	-4	-10	-14	-10	8	8	-4	-4	16	-4	-10	-6

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Quadratic twists for elliptic curve 1078f1

-4	8	-3	5	-7	-11
8624u1	34496u1	9702bw1	26950cv1	154c1	11858bm1

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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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