Cremona's table of elliptic curves

6600 = 2³ · 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 11+	Signs for the Atkin-Lehner involutions
Class	6600a	Isogeny class
Conductor	6600	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-451068750000 = -1 · 24 · 38 · 58 · 11	Discriminant
Eigenvalues	2+ 3+ 5+  0 11+  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1617,-20988]	[a1,a2,a3,a4,a6]
Generators	[32:250:1]	Generators of the group modulo torsion
j	1869154304/1804275	j-invariant
L	3.4490294953967	L(r)(E,1)/r!
Ω	0.5119561216908	Real period
R	1.6842407724347	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	13200u1 52800cq1 19800bh1 1320m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6600a1

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

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Quadratic twists for elliptic curve 6600a1

-4	8	-3	5	-11
13200u1	52800cq1	19800bh1	1320m1	72600ck1

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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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