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	4046h	Isogeny class
Conductor	4046	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	34816	Modular degree for the optimal curve
Δ	72890749816140032 = 28 · 74 · 179	Discriminant
Eigenvalues	2-  0  0 7+  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-219550,37459245]	[a1,a2,a3,a4,a6]
j	9869198625/614656	j-invariant
L	2.7164083341303	L(r)(E,1)/r!
Ω	0.33955104176629	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32368v1 129472a1 36414p1 101150p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4046h1

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
-	0	0	+	0	2	+	-4	8	8	8	-8	8	4	-8	10	12	0	-4	-8	8	8	4	6	8

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Quadratic twists for elliptic curve 4046h1

-4	8	-3	5	-7	17
32368v1	129472a1	36414p1	101150p1	28322q1	4046o1

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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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