Cremona's table of elliptic curves

2601 = 3² · 17²

Field	Data	Notes
Atkin-Lehner	3+ 17-	Signs for the Atkin-Lehner involutions
Class	2601f	Isogeny class
Conductor	2601	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	7344	Modular degree for the optimal curve
Δ	-137303833711203 = -1 · 39 · 178	Discriminant
Eigenvalues	-1 3+ -2  1  6  1 17-  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-8291,636310]	[a1,a2,a3,a4,a6]
j	-459	j-invariant
L	1.0349571218781	L(r)(E,1)/r!
Ω	0.51747856093907	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	41616bv1 2601e1 65025q1 127449p1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2601f1

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	1	6	1	-	5	-2	-6	7	7	-6	7	-12	12	-6	11	-11	2	-6	0	2	16	17

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Quadratic twists for elliptic curve 2601f1

-4	-3	5	-7	17
41616bv1	2601e1	65025q1	127449p1	2601b1

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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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