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	4758i	Isogeny class
Conductor	4758	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	55174828919808 = 210 · 3 · 136 · 612	Discriminant
Eigenvalues	2- 3-  4  4 -4 13+ -4  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-19176,955968]	[a1,a2,a3,a4,a6]
j	779828657309278849/55174828919808	j-invariant
L	6.162230464404	L(r)(E,1)/r!
Ω	0.6162230464404	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	38064u2 14274i2 118950k2 61854k2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4758i2

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

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Quadratic twists for elliptic curve 4758i2

-4	-3	5	13
38064u2	14274i2	118950k2	61854k2

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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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