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	25872bx	Isogeny class
Conductor	25872	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	-6507740378801958912 = -1 · 212 · 32 · 77 · 118	Discriminant
Eigenvalues	2- 3+  2 7- 11- -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,24288,-122735808]	[a1,a2,a3,a4,a6]
j	3288008303/13504609503	j-invariant
L	1.7606760228146	L(r)(E,1)/r!
Ω	0.11004225142593	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1617g6 103488hy5 77616fk5 3696w6	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872bx5

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	-2	4	0	-2	8	6	-10	4	-8	6	4	10	12	0	-2	-16	4	-18	-2

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Quadratic twists for elliptic curve 25872bx5

-4	8	-3	-7
1617g6	103488hy5	77616fk5	3696w6

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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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