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	8778g	Isogeny class
Conductor	8778	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	30576	Modular degree for the optimal curve
Δ	-9462159286272 = -1 · 213 · 37 · 7 · 11 · 193	Discriminant
Eigenvalues	2+ 3+  4 7- 11- -1  0 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3703,170005]	[a1,a2,a3,a4,a6]
j	-5617823470447609/9462159286272	j-invariant
L	1.9557761977575	L(r)(E,1)/r!
Ω	0.65192539925252	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	70224cg1 26334bq1 61446bf1 96558bx1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 8778g1

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
+	+	4	-	-	-1	0	-	-1	5	-4	-5	-9	12	10	-2	-6	-8	-2	6	3	12	-6	0	7

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Quadratic twists for elliptic curve 8778g1

-4	-3	-7	-11
70224cg1	26334bq1	61446bf1	96558bx1

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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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