Cremona's table of elliptic curves

2392 = 2³ · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 13+ 23-	Signs for the Atkin-Lehner involutions
Class	2392a	Isogeny class
Conductor	2392	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-2380212224 = -1 · 211 · 133 · 232	Discriminant
Eigenvalues	2- -1 -1 -1  2 13+  7  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,304,-1268]	[a1,a2,a3,a4,a6]
Generators	[9:46:1]	Generators of the group modulo torsion
j	1512116062/1162213	j-invariant
L	2.4679149153778	L(r)(E,1)/r!
Ω	0.81031043447192	Real period
R	1.5228206440327	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4784a1 19136n1 21528a1 59800c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2392a1

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	-1	-1	2	+	7	0	-	4	0	-1	-6	-1	1	-6	-4	-4	-10	7	0	0	-6	-14	-8

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Quadratic twists for elliptic curve 2392a1

-4	8	-3	5	-7	13	-23
4784a1	19136n1	21528a1	59800c1	117208t1	31096a1	55016d1

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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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