Cremona's table of elliptic curves

67032 = 2³ · 3² · 7² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 19-	Signs for the Atkin-Lehner involutions
Class	67032k	Isogeny class
Conductor	67032	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	138240	Modular degree for the optimal curve
Δ	-69343806185136 = -1 · 24 · 36 · 74 · 195	Discriminant
Eigenvalues	2+ 3-  1 7+  1  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-33222,-2364887]	[a1,a2,a3,a4,a6]
Generators	[224:1197:1]	Generators of the group modulo torsion
j	-144797599744/2476099	j-invariant
L	7.4162986911622	L(r)(E,1)/r!
Ω	0.17663317072653	Real period
R	0.69978349866148	Regulator
r	1	Rank of the group of rational points
S	0.99999999996241	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7448n1 67032t1	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 67032k1

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	2	2	-	3	-4	4	-10	-10	1	-1	4	-8	3	-4	4	-3	14	9	-6	-14

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Quadratic twists for elliptic curve 67032k1

-3	-7
7448n1	67032t1

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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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