Cremona's table of elliptic curves

9888 = 2⁵ · 3 · 103

Field	Data	Notes
Atkin-Lehner	2+ 3+ 103-	Signs for the Atkin-Lehner involutions
Class	9888b	Isogeny class
Conductor	9888	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	15488	Modular degree for the optimal curve
Δ	-74736193536 = -1 · 212 · 311 · 103	Discriminant
Eigenvalues	2+ 3+ -3  4  0 -1 -8  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3457,-78191]	[a1,a2,a3,a4,a6]
j	-1115802998848/18246141	j-invariant
L	1.24400599396	L(r)(E,1)/r!
Ω	0.31100149849001	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	9888d1 19776bg1 29664i1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 9888b1

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
+	+	-3	4	0	-1	-8	8	3	-8	5	-4	6	-7	4	2	3	-1	11	0	-6	12	-9	6	5

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Quadratic twists for elliptic curve 9888b1

-4	8	-3
9888d1	19776bg1	29664i1

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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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