Cremona's table of elliptic curves

4392 = 2³ · 3² · 61

Field	Data	Notes
Atkin-Lehner	2+ 3- 61-	Signs for the Atkin-Lehner involutions
Class	4392c	Isogeny class
Conductor	4392	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-39243987130032 = -1 · 24 · 311 · 614	Discriminant
Eigenvalues	2+ 3-  2  0  0 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-10434,-509047]	[a1,a2,a3,a4,a6]
Generators	[1468490:56132993:1000]	Generators of the group modulo torsion
j	-10770322266112/3364539363	j-invariant
L	4.1170395272662	L(r)(E,1)/r!
Ω	0.2324717053897	Real period
R	8.8549260658725	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8784d1 35136n1 1464f1 109800br1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4392c1

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

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Quadratic twists for elliptic curve 4392c1

-4	8	-3	5
8784d1	35136n1	1464f1	109800br1

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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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