Cremona's table of elliptic curves

99 = 3² · 11

Field	Data	Notes
Atkin-Lehner	3+ 11+	Signs for the Atkin-Lehner involutions
Class	99a	Isogeny class
Conductor	99	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4	Modular degree for the optimal curve
Δ	297 = 33 · 11	Discriminant
Eigenvalues	-1 3+ -4 -2 11+ -2  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2,0]	[a1,a2,a3,a4,a6]
Generators	[0:0:1]	Generators of the group modulo torsion
j	19683/11	j-invariant
L	0.68055155913983	L(r)(E,1)/r!
Ω	4.4984528865883	Real period
R	0.3025713845615	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1584k1 6336j1 99c1 2475a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 99a1

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
-1	+	-4	-2	+	-2	2	-6	4	-6	4	-6	-10	6	-8	0	4	-6	8	0	-2	-10	12	0	2

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Quadratic twists for elliptic curve 99a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1584k1	6336j1	99c1	2475a1	4851d1	1089c1	16731d1	28611e1	35739e1	52371b1	83259d1	95139b1

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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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