Cremona's table of elliptic curves

19320 = 2³ · 3 · 5 · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7- 23-	Signs for the Atkin-Lehner involutions
Class	19320q	Isogeny class
Conductor	19320	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	511902720 = 210 · 33 · 5 · 7 · 232	Discriminant
Eigenvalues	2- 3+ 5+ 7-  6 -2 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-376,2716]	[a1,a2,a3,a4,a6]
j	5756278756/499905	j-invariant
L	1.610302933368	L(r)(E,1)/r!
Ω	1.610302933368	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	38640p1 57960w1 96600bb1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 19320q1

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

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Quadratic twists for elliptic curve 19320q1

-4	-3	5
38640p1	57960w1	96600bb1

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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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