Cremona's table of elliptic curves

25992 = 2³ · 3² · 19²

Field	Data	Notes
Atkin-Lehner	2+ 3- 19-	Signs for the Atkin-Lehner involutions
Class	25992k	Isogeny class
Conductor	25992	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	138240	Modular degree for the optimal curve
Δ	4504083824316672 = 28 · 39 · 197	Discriminant
Eigenvalues	2+ 3- -2  0  0 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-559911,-161227654]	[a1,a2,a3,a4,a6]
Generators	[192470:6407028:125]	Generators of the group modulo torsion
j	2211014608/513	j-invariant
L	4.2072029427442	L(r)(E,1)/r!
Ω	0.17453231593527	Real period
R	6.0263953414573	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	51984x1 8664i1 1368g1	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 25992k1

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

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Quadratic twists for elliptic curve 25992k1

-4	-3	-19
51984x1	8664i1	1368g1

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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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