Cremona's table of elliptic curves

6612 = 2² · 3 · 19 · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 19- 29+	Signs for the Atkin-Lehner involutions
Class	6612a	Isogeny class
Conductor	6612	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1200	Modular degree for the optimal curve
Δ	-40703472 = -1 · 24 · 35 · 192 · 29	Discriminant
Eigenvalues	2- 3+  0  1 -3 -1  5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-38,333]	[a1,a2,a3,a4,a6]
Generators	[7:19:1]	Generators of the group modulo torsion
j	-389344000/2543967	j-invariant
L	3.4777063037995	L(r)(E,1)/r!
Ω	1.7564718878498	Real period
R	0.98996924683398	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	26448p1 105792q1 19836i1 125628k1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 6612a1

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	1	-3	-1	5	-	0	+	-4	2	-6	12	1	12	-12	-14	13	4	-8	0	-2	-3	-10

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Quadratic twists for elliptic curve 6612a1

-4	8	-3	-19
26448p1	105792q1	19836i1	125628k1

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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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