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	23712g	Isogeny class
Conductor	23712	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	81948672 = 212 · 34 · 13 · 19	Discriminant
Eigenvalues	2+ 3- -2  0  4 13+ -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1329,18207]	[a1,a2,a3,a4,a6]
Generators	[9:84:1]	Generators of the group modulo torsion
j	63425726272/20007	j-invariant
L	5.7768392711516	L(r)(E,1)/r!
Ω	1.8837100503386	Real period
R	1.5333674283134	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	23712a4 47424cj1 71136bd4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 23712g4

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

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Quadratic twists for elliptic curve 23712g4

-4	8	-3
23712a4	47424cj1	71136bd4

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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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