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	4641a	Isogeny class
Conductor	4641	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	4641 = 3 · 7 · 13 · 17	Discriminant
Eigenvalues	-1 3+  2 7+  4 13- 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-24752,-1509184]	[a1,a2,a3,a4,a6]
Generators	[415:7532:1]	Generators of the group modulo torsion
j	1677087406638588673/4641	j-invariant
L	2.3701611465513	L(r)(E,1)/r!
Ω	0.38062463122656	Real period
R	6.2270303918943	Regulator
r	1	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	74256dc4 13923g3 116025bf4 32487n4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4641a3

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	+	4	-	-	4	-8	-6	-8	2	6	-4	-12	6	0	-14	8	-8	2	8	0	-14	10

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Quadratic twists for elliptic curve 4641a3

-4	-3	5	-7	13	17
74256dc4	13923g3	116025bf4	32487n4	60333e4	78897m4

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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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