Cremona's table of elliptic curves

6699 = 3 · 7 · 11 · 29

Field	Data	Notes
Atkin-Lehner	3+ 7+ 11- 29-	Signs for the Atkin-Lehner involutions
Class	6699d	Isogeny class
Conductor	6699	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	20736	Modular degree for the optimal curve
Δ	-52843101620463 = -1 · 36 · 7 · 114 · 294	Discriminant
Eigenvalues	-1 3+ -2 7+ 11-  2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-33814,2404610]	[a1,a2,a3,a4,a6]
Generators	[62:711:1]	Generators of the group modulo torsion
j	-4275768267198290017/52843101620463	j-invariant
L	1.6479495133507	L(r)(E,1)/r!
Ω	0.63328460023285	Real period
R	1.3011128904325	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	107184ct1 20097f1 46893r1 73689m1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6699d1

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
-1	+	-2	+	-	2	2	-8	0	-	0	-2	2	4	8	-10	0	6	-12	8	2	8	-12	6	-2

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Quadratic twists for elliptic curve 6699d1

-4	-3	-7	-11
107184ct1	20097f1	46893r1	73689m1

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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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