Cremona's table of elliptic curves

99 = 3² · 11

Field	Data	Notes
Atkin-Lehner	3- 11+	Signs for the Atkin-Lehner involutions
Class	99b	Isogeny class
Conductor	99	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-4261625379 = -1 · 318 · 11	Discriminant
Eigenvalues	-1 3-  2  4 11+ -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,391,-1092]	[a1,a2,a3,a4,a6]
j	9090072503/5845851	j-invariant
L	0.79230740387988	L(r)(E,1)/r!
Ω	0.79230740387988	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1584q4 6336bd4 33a4 2475g4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 99b4

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	-	2	4	+	-2	2	0	-8	6	-8	6	2	0	-8	-6	4	6	-4	0	-14	-4	-12	6	2

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Quadratic twists for elliptic curve 99b4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1584q4	6336bd4	33a4	2475g4	4851j4	1089g4	16731k4	28611u3	35739q3	52371e3	83259l3	95139j3

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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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