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	4758b	Isogeny class
Conductor	4758	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-7546188 = -1 · 22 · 3 · 132 · 612	Discriminant
Eigenvalues	2+ 3+ -4  0 -4 13- -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,48,60]	[a1,a2,a3,a4,a6]
Generators	[-1:4:1] [2:12:1]	Generators of the group modulo torsion
j	11836763639/7546188	j-invariant
L	2.6840598698196	L(r)(E,1)/r!
Ω	1.4605323965025	Real period
R	0.91886351725166	Regulator
r	2	Rank of the group of rational points
S	0.9999999999996	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	38064be2 14274t2 118950bn2 61854n2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4758b2

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

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Quadratic twists for elliptic curve 4758b2

-4	-3	5	13
38064be2	14274t2	118950bn2	61854n2

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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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