Cremona's table of elliptic curves

4758 = 2 · 3 · 13 · 61

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 61-	Signs for the Atkin-Lehner involutions
Class	4758f	Isogeny class
Conductor	4758	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	12096	Modular degree for the optimal curve
Δ	10255986503568 = 24 · 314 · 133 · 61	Discriminant
Eigenvalues	2- 3+  0  0 -4 13+  8 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5708,59357]	[a1,a2,a3,a4,a6]
Generators	[5:173:1]	Generators of the group modulo torsion
j	20567445764946625/10255986503568	j-invariant
L	4.6644413477312	L(r)(E,1)/r!
Ω	0.64076800324997	Real period
R	3.6397271118979	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	38064bc1 14274g1 118950z1 61854d1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4758f1

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	0	-4	+	8	-2	-4	0	-4	10	-12	-2	8	0	-4	-	8	-16	6	-10	-16	14	-10

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Quadratic twists for elliptic curve 4758f1

-4	-3	5	13
38064bc1	14274g1	118950z1	61854d1

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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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