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	16	Product of Tamagawa factors cp
Δ	21538881 = 32 · 72 · 132 · 172	Discriminant
Eigenvalues	-1 3+  2 7+  4 13- 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1547,-24064]	[a1,a2,a3,a4,a6]
Generators	[58:263:1]	Generators of the group modulo torsion
j	409460675852593/21538881	j-invariant
L	2.3701611465513	L(r)(E,1)/r!
Ω	0.76124926245312	Real period
R	3.1135151959471	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	74256dc2 13923g2 116025bf2 32487n2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4641a2

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 4641a2

-4	-3	5	-7	13	17
74256dc2	13923g2	116025bf2	32487n2	60333e2	78897m2

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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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