Cremona's table of elliptic curves

25872 = 2⁴ · 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	25872k	Isogeny class
Conductor	25872	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-21913584 = -1 · 24 · 3 · 73 · 113	Discriminant
Eigenvalues	2+ 3+  3 7- 11- -5  4  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-44,267]	[a1,a2,a3,a4,a6]
Generators	[19:77:1]	Generators of the group modulo torsion
j	-1755904/3993	j-invariant
L	5.8232083044022	L(r)(E,1)/r!
Ω	1.9043039678247	Real period
R	0.50965325588698	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	12936y1 103488ia1 77616bx1 25872y1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872k1

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
+	+	3	-	-	-5	4	1	2	5	4	-3	6	-4	-13	-6	-9	-2	-5	-6	-7	-8	-8	-2	-8

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Quadratic twists for elliptic curve 25872k1

-4	8	-3	-7
12936y1	103488ia1	77616bx1	25872y1

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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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