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	12	Product of Tamagawa factors cp
Δ	1412270047483064 = 23 · 77 · 118	Discriminant
Eigenvalues	2-  0 -2 7- 11+ -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-29581,-744579]	[a1,a2,a3,a4,a6]
Generators	[-47:758:1]	Generators of the group modulo torsion
j	24331017010833/12004097336	j-invariant
L	3.1585369241262	L(r)(E,1)/r!
Ω	0.38288274136866	Real period
R	2.7497861032123	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	8624w4 34496bd3 9702w4 26950g3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1078i3

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 1078i3

-4	8	-3	5	-7	-11
8624w4	34496bd3	9702w4	26950g3	154b4	11858i4

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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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