Cremona's table of elliptic curves

4046 = 2 · 7 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 7- 17+	Signs for the Atkin-Lehner involutions
Class	4046f	Isogeny class
Conductor	4046	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	68544	Modular degree for the optimal curve
Δ	3612661069604608 = 28 · 7 · 1710	Discriminant
Eigenvalues	2+  3  2 7-  2 -6 17+  7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-99181,11694245]	[a1,a2,a3,a4,a6]
j	53520777/1792	j-invariant
L	3.5281431752157	L(r)(E,1)/r!
Ω	0.44101789690196	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32368m1 129472bj1 36414cv1 101150bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4046f1

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
+	3	2	-	2	-6	+	7	8	9	-5	-2	0	-8	-7	-3	1	2	-10	8	4	16	-3	-6	-10

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Quadratic twists for elliptic curve 4046f1

-4	8	-3	5	-7	17
32368m1	129472bj1	36414cv1	101150bv1	28322k1	4046d1

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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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