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	6612c	Isogeny class
Conductor	6612	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-30961933056 = -1 · 28 · 32 · 19 · 294	Discriminant
Eigenvalues	2- 3-  1  1 -5 -2  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,435,-7569]	[a1,a2,a3,a4,a6]
Generators	[29:174:1]	Generators of the group modulo torsion
j	35477479424/120945051	j-invariant
L	5.0832013341147	L(r)(E,1)/r!
Ω	0.59805986292736	Real period
R	0.35414524317248	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	26448k1 105792c1 19836f1 125628a1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 6612c1

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	1	-5	-2	3	-	-4	-	-6	-4	0	5	9	-6	0	-1	4	-16	1	-16	-4	-14	14

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Quadratic twists for elliptic curve 6612c1

-4	8	-3	-19
26448k1	105792c1	19836f1	125628a1

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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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