Cremona's table of elliptic curves

4690 = 2 · 5 · 7 · 67

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 67-	Signs for the Atkin-Lehner involutions
Class	4690c	Isogeny class
Conductor	4690	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	9853103750 = 2 · 54 · 76 · 67	Discriminant
Eigenvalues	2- -2 5+ 7+  0  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-536,-134]	[a1,a2,a3,a4,a6]
Generators	[198:251:8]	Generators of the group modulo torsion
j	17032120495489/9853103750	j-invariant
L	3.6090801106295	L(r)(E,1)/r!
Ω	1.0872127335122	Real period
R	3.319571229607	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	37520g2 42210m2 23450f2 32830o2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4690c2

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

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Quadratic twists for elliptic curve 4690c2

-4	-3	5	-7
37520g2	42210m2	23450f2	32830o2

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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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