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	4758g	Isogeny class
Conductor	4758	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	147992832 = 28 · 36 · 13 · 61	Discriminant
Eigenvalues	2- 3+ -2  0 -4 13- -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-12049,504047]	[a1,a2,a3,a4,a6]
j	193454563071992977/147992832	j-invariant
L	1.5223617982441	L(r)(E,1)/r!
Ω	1.5223617982441	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	38064bg1 14274l1 118950r1 61854e1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4758g1

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

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Quadratic twists for elliptic curve 4758g1

-4	-3	5	13
38064bg1	14274l1	118950r1	61854e1

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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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