Cremona's table of elliptic curves

658 = 2 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2+ 7+ 47-	Signs for the Atkin-Lehner involutions
Class	658a	Isogeny class
Conductor	658	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	5040	Modular degree for the optimal curve
Δ	-41560810459234304 = -1 · 230 · 77 · 47	Discriminant
Eigenvalues	2+ -1 -1 7+  1  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-117008,18214144]	[a1,a2,a3,a4,a6]
j	-177164286626930705929/41560810459234304	j-invariant
L	0.69071408948834	L(r)(E,1)/r!
Ω	0.34535704474417	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	5264h1 21056d1 5922n1 16450m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 658a1

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	-1	+	1	2	0	-2	8	8	-4	-1	9	5	-	1	15	-12	16	-2	13	14	-1	0	-8

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Quadratic twists for elliptic curve 658a1

-4	8	-3	5	-7	-11	13	-47
5264h1	21056d1	5922n1	16450m1	4606b1	79618be1	111202w1	30926c1

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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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