Cremona's table of elliptic curves

4263 = 3 · 7² · 29

Field	Data	Notes
Atkin-Lehner	3+ 7- 29-	Signs for the Atkin-Lehner involutions
Class	4263c	Isogeny class
Conductor	4263	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	268569 = 33 · 73 · 29	Discriminant
Eigenvalues	1 3+ -2 7-  0  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-116,435]	[a1,a2,a3,a4,a6]
Generators	[10:15:1]	Generators of the group modulo torsion
j	510082399/783	j-invariant
L	3.2472213400167	L(r)(E,1)/r!
Ω	3.0960173570147	Real period
R	2.0976764440027	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	68208ct1 12789h1 106575cg1 4263f1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4263c1

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
1	+	-2	-	0	4	0	-4	6	-	0	6	0	10	0	2	-12	-14	-4	-6	-10	-10	4	12	-2

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Quadratic twists for elliptic curve 4263c1

-4	-3	5	-7	29
68208ct1	12789h1	106575cg1	4263f1	123627s1

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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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