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	3300h	Isogeny class
Conductor	3300	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	36085500000000 = 28 · 38 · 59 · 11	Discriminant
Eigenvalues	2- 3+ 5-  2 11-  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-10708,-310088]	[a1,a2,a3,a4,a6]
j	271593488/72171	j-invariant
L	1.9144601433662	L(r)(E,1)/r!
Ω	0.47861503584155	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13200cp2 52800dn2 9900x2 3300r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3300h2

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 3300h2

-4	8	-3	5	-11
13200cp2	52800dn2	9900x2	3300r2	36300bc2

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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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