Cremona's table of elliptic curves

4680 = 2³ · 3² · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 13+	Signs for the Atkin-Lehner involutions
Class	4680m	Isogeny class
Conductor	4680	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	-449280 = -1 · 28 · 33 · 5 · 13	Discriminant
Eigenvalues	2- 3+ 5-  3 -5 13+  3 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12,36]	[a1,a2,a3,a4,a6]
Generators	[0:6:1]	Generators of the group modulo torsion
j	-27648/65	j-invariant
L	4.1598021152419	L(r)(E,1)/r!
Ω	2.6301417950922	Real period
R	0.39539713438682	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9360f1 37440l1 4680a1 23400e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4680m1

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
-	+	-	3	-5	+	3	-8	3	2	-10	-3	-3	-10	6	-5	-4	-7	12	-5	2	-13	12	7	-5

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Quadratic twists for elliptic curve 4680m1

-4	8	-3	5	13
9360f1	37440l1	4680a1	23400e1	60840a1

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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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