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	1078i	Isogeny class
Conductor	1078	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	5401756892224 = 26 · 78 · 114	Discriminant
Eigenvalues	2-  0 -2 7- 11+ -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-15861,764621]	[a1,a2,a3,a4,a6]
Generators	[-19:1038:1]	Generators of the group modulo torsion
j	3750606459153/45914176	j-invariant
L	3.1585369241262	L(r)(E,1)/r!
Ω	0.76576548273732	Real period
R	1.3748930516062	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8624w2 34496bd2 9702w2 26950g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1078i2

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
-	0	-2	-	+	-2	-2	0	-8	-2	8	-2	-10	4	-8	6	0	-10	-12	16	14	0	0	6	-10

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Quadratic twists for elliptic curve 1078i2

-4	8	-3	5	-7	-11
8624w2	34496bd2	9702w2	26950g2	154b2	11858i2

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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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