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	4680f	Isogeny class
Conductor	4680	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	-6422411112577200 = -1 · 24 · 39 · 52 · 138	Discriminant
Eigenvalues	2+ 3- 5+  0  4 13- -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-83658,-10080007]	[a1,a2,a3,a4,a6]
Generators	[389:4030:1]	Generators of the group modulo torsion
j	-5551350318708736/550618236675	j-invariant
L	3.6590615994393	L(r)(E,1)/r!
Ω	0.13957466975049	Real period
R	3.2769749750978	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	9360l1 37440cc1 1560j1 23400bh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4680f1

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
+	-	+	0	4	-	-2	-4	-8	-6	8	6	-2	-12	8	2	-12	-2	12	-16	10	8	12	-18	2

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Quadratic twists for elliptic curve 4680f1

-4	8	-3	5	13
9360l1	37440cc1	1560j1	23400bh1	60840br1

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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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