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	4046m	Isogeny class
Conductor	4046	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-64736 = -1 · 25 · 7 · 172	Discriminant
Eigenvalues	2-  3  1 7+  0  1 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-12,-17]	[a1,a2,a3,a4,a6]
j	-610929/224	j-invariant
L	6.3389935244302	L(r)(E,1)/r!
Ω	1.267798704886	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	32368bh1 129472q1 36414r1 101150x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4046m1

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	1	+	0	1	+	4	-3	-6	6	12	-6	12	-10	4	4	13	0	-15	-8	8	-15	-2	2

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Quadratic twists for elliptic curve 4046m1

-4	8	-3	5	-7	17
32368bh1	129472q1	36414r1	101150x1	28322be1	4046t1

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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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