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	25872q	Isogeny class
Conductor	25872	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	515451795167232 = 211 · 34 · 710 · 11	Discriminant
Eigenvalues	2+ 3- -2 7- 11+ -6 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1863584,-979821228]	[a1,a2,a3,a4,a6]
Generators	[-788:6:1]	Generators of the group modulo torsion
j	2970658109581346/2139291	j-invariant
L	4.9091342995195	L(r)(E,1)/r!
Ω	0.12921481518351	Real period
R	2.3745024383174	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	12936t4 103488gj4 77616ck4 3696d4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872q4

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	-	+	-6	-6	0	8	-2	4	-2	2	12	12	6	4	-6	-4	0	2	-8	0	6	-18

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Quadratic twists for elliptic curve 25872q4

-4	8	-3	-7
12936t4	103488gj4	77616ck4	3696d4

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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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