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	25872b	Isogeny class
Conductor	25872	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	79488	Modular degree for the optimal curve
Δ	-1463891159808 = -1 · 28 · 39 · 74 · 112	Discriminant
Eigenvalues	2+ 3+ -4 7+ 11- -5 -6  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5945,-183819]	[a1,a2,a3,a4,a6]
j	-37811178496/2381643	j-invariant
L	0.54172136613663	L(r)(E,1)/r!
Ω	0.27086068306835	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12936h1 103488ha1 77616bf1 25872ba1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872b1

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
+	+	-4	+	-	-5	-6	7	8	-2	1	-5	-12	-1	2	2	0	6	11	-12	-9	-7	16	6	2

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Quadratic twists for elliptic curve 25872b1

-4	8	-3	-7
12936h1	103488ha1	77616bf1	25872ba1

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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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