Cremona's table of elliptic curves

8778 = 2 · 3 · 7 · 11 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 11+ 19+	Signs for the Atkin-Lehner involutions
Class	8778i	Isogeny class
Conductor	8778	Conductor
∏ cp	42	Product of Tamagawa factors cp
deg	6048	Modular degree for the optimal curve
Δ	-10033886016 = -1 · 26 · 37 · 73 · 11 · 19	Discriminant
Eigenvalues	2+ 3-  1 7- 11+ -2  0 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,172,4754]	[a1,a2,a3,a4,a6]
Generators	[9:79:1]	Generators of the group modulo torsion
j	567457901639/10033886016	j-invariant
L	4.1692402640023	L(r)(E,1)/r!
Ω	0.96017038015966	Real period
R	0.10338542761221	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	70224bm1 26334br1 61446h1 96558ct1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 8778i1

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	-	+	-2	0	+	-1	-4	2	-10	-3	11	12	-5	-7	1	-12	12	-3	-14	-4	0	-15

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Quadratic twists for elliptic curve 8778i1

-4	-3	-7	-11
70224bm1	26334br1	61446h1	96558ct1

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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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