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
deg	12	Modular degree for the optimal curve
Δ	216513 = 39 · 11	Discriminant
Eigenvalues	-1 3-  2  4 11+ -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-59,186]	[a1,a2,a3,a4,a6]
j	30664297/297	j-invariant
L	0.79230740387988	L(r)(E,1)/r!
Ω	3.1692296155195	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	1584q1 6336bd1 33a2 2475g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 99b1

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 99b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1584q1	6336bd1	33a2	2475g1	4851j1	1089g1	16731k1	28611u1	35739q1	52371e1	83259l1	95139j1

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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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