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	25872bc	Isogeny class
Conductor	25872	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	145152	Modular degree for the optimal curve
Δ	-13577070414200832 = -1 · 216 · 33 · 78 · 113	Discriminant
Eigenvalues	2- 3+  0 7+ 11+ -4  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-47448,6889968]	[a1,a2,a3,a4,a6]
j	-500313625/574992	j-invariant
L	0.72035091557548	L(r)(E,1)/r!
Ω	0.36017545778779	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	3234j1 103488hd1 77616ep1 25872cj1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872bc1

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
-	+	0	+	+	-4	3	1	3	-9	-2	-7	-6	-11	3	0	-9	-10	4	-3	-4	16	0	0	-1

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Quadratic twists for elliptic curve 25872bc1

-4	8	-3	-7
3234j1	103488hd1	77616ep1	25872cj1

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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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