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	3300m	Isogeny class
Conductor	3300	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-618750000 = -1 · 24 · 32 · 58 · 11	Discriminant
Eigenvalues	2- 3- 5+  0 11-  4  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-33,1188]	[a1,a2,a3,a4,a6]
j	-16384/2475	j-invariant
L	2.6601026563288	L(r)(E,1)/r!
Ω	1.3300513281644	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	13200bh1 52800e1 9900j1 660b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3300m1

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
-	-	+	0	-	4	2	2	8	-4	-4	2	-12	-8	4	10	4	6	-12	0	16	6	2	18	2

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Quadratic twists for elliptic curve 3300m1

-4	8	-3	5	-11
13200bh1	52800e1	9900j1	660b1	36300bj1

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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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