Cremona's table of elliptic curves

4641 = 3 · 7 · 13 · 17

Field	Data	Notes
Atkin-Lehner	3- 7+ 13- 17+	Signs for the Atkin-Lehner involutions
Class	4641d	Isogeny class
Conductor	4641	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	710073 = 33 · 7 · 13 · 172	Discriminant
Eigenvalues	1 3-  0 7+  4 13- 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-46,107]	[a1,a2,a3,a4,a6]
Generators	[7:8:1]	Generators of the group modulo torsion
j	10431681625/710073	j-invariant
L	5.2540808388418	L(r)(E,1)/r!
Ω	2.8032508452067	Real period
R	1.2495209143403	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	74256ce1 13923j1 116025l1 32487f1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4641d1

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

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Quadratic twists for elliptic curve 4641d1

-4	-3	5	-7	13	17
74256ce1	13923j1	116025l1	32487f1	60333n1	78897g1

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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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