Cremona's table of elliptic curves

4248 = 2³ · 3² · 59

Field	Data	Notes
Atkin-Lehner	2- 3+ 59-	Signs for the Atkin-Lehner involutions
Class	4248f	Isogeny class
Conductor	4248	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	1631232 = 210 · 33 · 59	Discriminant
Eigenvalues	2- 3+ -2  0  4  0  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-51,126]	[a1,a2,a3,a4,a6]
Generators	[-5:16:1]	Generators of the group modulo torsion
j	530604/59	j-invariant
L	3.3554441187635	L(r)(E,1)/r!
Ω	2.5817606703001	Real period
R	1.2996727997927	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	8496a1 33984b1 4248a1 106200c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4248f1

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

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Quadratic twists for elliptic curve 4248f1

-4	8	-3	5
8496a1	33984b1	4248a1	106200c1

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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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