Cremona's table of elliptic curves

25392 = 2⁴ · 3 · 23²

Field	Data	Notes
Atkin-Lehner	2+ 3- 23-	Signs for the Atkin-Lehner involutions
Class	25392h	Isogeny class
Conductor	25392	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	52992	Modular degree for the optimal curve
Δ	-541285530262272 = -1 · 28 · 33 · 238	Discriminant
Eigenvalues	2+ 3-  2  1 -2  1 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,16223,-782293]	[a1,a2,a3,a4,a6]
Generators	[1578:16399:27]	Generators of the group modulo torsion
j	23552/27	j-invariant
L	7.7734476850116	L(r)(E,1)/r!
Ω	0.27985625552816	Real period
R	3.0862858784974	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	12696k1 101568cn1 76176p1 25392o1	Quadratic twists by: -4 8 -3 -23

Hecke Eigenvalues for elliptic curve 25392h1

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	1	-2	1	-2	0	-	-2	0	-1	0	1	-4	-6	-8	-1	-5	8	-6	0	6	-8	10

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Quadratic twists for elliptic curve 25392h1

-4	8	-3	-23
12696k1	101568cn1	76176p1	25392o1

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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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