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	128	Product of Tamagawa factors cp
Δ	798636202552387584 = 211 · 316 · 77 · 11	Discriminant
Eigenvalues	2+ 3- -2 7- 11+ -6 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-268144,31653236]	[a1,a2,a3,a4,a6]
Generators	[-565:1764:1]	Generators of the group modulo torsion
j	8849350367426/3314597517	j-invariant
L	4.9091342995195	L(r)(E,1)/r!
Ω	0.25842963036702	Real period
R	2.3745024383174	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12936t3 103488gj3 77616ck3 3696d3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872q3

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 25872q3

-4	8	-3	-7
12936t3	103488gj3	77616ck3	3696d3

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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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