Cremona's table of elliptic curves

99099 = 3² · 7 · 11² · 13

Field	Data	Notes
Atkin-Lehner	3+ 7+ 11- 13+	Signs for the Atkin-Lehner involutions
Class	99099f	Isogeny class
Conductor	99099	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	53760	Modular degree for the optimal curve
Δ	467648181 = 33 · 7 · 114 · 132	Discriminant
Eigenvalues	-2 3+ -1 7+ 11- 13+  5  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-363,2450]	[a1,a2,a3,a4,a6]
Generators	[-21:28:1] [-11:71:1]	Generators of the group modulo torsion
j	13381632/1183	j-invariant
L	5.5877054695552	L(r)(E,1)/r!
Ω	1.6217168966262	Real period
R	0.28712910587823	Regulator
r	2	Rank of the group of rational points
S	0.99999999988627	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	99099e1 99099k1	Quadratic twists by: -3 -11

Hecke Eigenvalues for elliptic curve 99099f1

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
-2	+	-1	+	-	+	5	2	-6	0	-10	-6	6	-9	-1	-2	3	-8	-9	0	2	12	-11	5	-14

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Quadratic twists for elliptic curve 99099f1

-3	-11
99099e1	99099k1

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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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