Cremona's table of elliptic curves

3300 = 2² · 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 11-	Signs for the Atkin-Lehner involutions
Class	3300r	Isogeny class
Conductor	3300	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	19602000 = 24 · 34 · 53 · 112	Discriminant
Eigenvalues	2- 3- 5- -2 11- -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-153,648]	[a1,a2,a3,a4,a6]
Generators	[-3:33:1]	Generators of the group modulo torsion
j	199344128/9801	j-invariant
L	3.8676001837718	L(r)(E,1)/r!
Ω	2.1404315103904	Real period
R	0.15057712136537	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	13200bw1 52800bq1 9900y1 3300h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3300r1

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	-	-2	-6	4	0	2	-8	0	-2	-2	-8	8	-8	10	-8	-12	-14	8	6	-14	-12

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Quadratic twists for elliptic curve 3300r1

-4	8	-3	5	-11
13200bw1	52800bq1	9900y1	3300h1	36300ci1

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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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