Cremona's table of elliptic curves

8690 = 2 · 5 · 11 · 79

Field	Data	Notes
Atkin-Lehner	2+ 5- 11- 79+	Signs for the Atkin-Lehner involutions
Class	8690c	Isogeny class
Conductor	8690	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	6480	Modular degree for the optimal curve
Δ	-1716275000 = -1 · 23 · 55 · 11 · 792	Discriminant
Eigenvalues	2+ -1 5- -3 11-  4 -5 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1507,21989]	[a1,a2,a3,a4,a6]
Generators	[43:176:1]	Generators of the group modulo torsion
j	-378890468381881/1716275000	j-invariant
L	2.4104574416502	L(r)(E,1)/r!
Ω	1.5004825091875	Real period
R	0.16064548749424	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	69520z1 78210bc1 43450t1 95590s1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 8690c1

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	-	-3	-	4	-5	-1	6	5	-7	-1	0	-6	-4	3	-6	7	12	-11	14	+	-4	-7	-2

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Quadratic twists for elliptic curve 8690c1

-4	-3	5	-11
69520z1	78210bc1	43450t1	95590s1

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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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