Cremona's table of elliptic curves

23712 = 2⁵ · 3 · 13 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 13+ 19-	Signs for the Atkin-Lehner involutions
Class	23712h	Isogeny class
Conductor	23712	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-73984562016768 = -1 · 29 · 38 · 132 · 194	Discriminant
Eigenvalues	2+ 3- -2 -4  4 13+  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7944,-498168]	[a1,a2,a3,a4,a6]
Generators	[138:1026:1]	Generators of the group modulo torsion
j	-108299418804296/144501097689	j-invariant
L	4.8842436541839	L(r)(E,1)/r!
Ω	0.24095072073338	Real period
R	2.5338395125556	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	23712k2 47424s3 71136be2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 23712h2

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

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Quadratic twists for elliptic curve 23712h2

-4	8	-3
23712k2	47424s3	71136be2

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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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