Cremona's table of elliptic curves

99 = 3² · 11

Field	Data	Notes
Atkin-Lehner	3+ 11-	Signs for the Atkin-Lehner involutions
Class	99c	Isogeny class
Conductor	99	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2381643 = 39 · 112	Discriminant
Eigenvalues	1 3+  4 -2 11- -2 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-150,-667]	[a1,a2,a3,a4,a6]
j	19034163/121	j-invariant
L	1.3642922956913	L(r)(E,1)/r!
Ω	1.3642922956913	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	1584i2 6336e2 99a2 2475d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 99c2

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 99c2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1584i2	6336e2	99a2	2475d2	4851f2	1089d2	16731b2	28611b2	35739j2	52371a2	83259a2	95139a2

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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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