Cremona's table of elliptic curves

25232 = 2⁴ · 19 · 83

Field	Data	Notes
Atkin-Lehner	2- 19- 83+	Signs for the Atkin-Lehner involutions
Class	25232k	Isogeny class
Conductor	25232	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	-479408 = -1 · 24 · 192 · 83	Discriminant
Eigenvalues	2- -1 -2 -1 -3  4 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9,-32]	[a1,a2,a3,a4,a6]
Generators	[12:38:1]	Generators of the group modulo torsion
j	-5619712/29963	j-invariant
L	2.8666434784985	L(r)(E,1)/r!
Ω	1.2290346260065	Real period
R	1.1662175409219	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	6308b1 100928t1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 25232k1

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	-2	-1	-3	4	-3	-	4	-1	5	3	2	-12	-6	6	9	-15	-8	4	-12	14	+	-6	-8

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Quadratic twists for elliptic curve 25232k1

-4	8
6308b1	100928t1

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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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