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	4641b	Isogeny class
Conductor	4641	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	6115533215337 = 32 · 72 · 138 · 17	Discriminant
Eigenvalues	-1 3+ -2 7+ -4 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-40579,-3160960]	[a1,a2,a3,a4,a6]
Generators	[-116:103:1]	Generators of the group modulo torsion
j	7389727131216686257/6115533215337	j-invariant
L	1.4038849798161	L(r)(E,1)/r!
Ω	0.33639206258239	Real period
R	0.52166992624576	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	74256dd6 13923f5 116025bg6 32487m6	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4641b5

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

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Quadratic twists for elliptic curve 4641b5

-4	-3	5	-7	13	17
74256dd6	13923f5	116025bg6	32487m6	60333d6	78897l6

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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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