Cremona's table of elliptic curves

33462 = 2 · 3² · 11 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 11+ 13-	Signs for the Atkin-Lehner involutions
Class	33462ba	Isogeny class
Conductor	33462	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	524160	Modular degree for the optimal curve
Δ	-3621916368267129504 = -1 · 25 · 36 · 114 · 139	Discriminant
Eigenvalues	2+ 3- -1  1 11+ 13- -1 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-334905,118189709]	[a1,a2,a3,a4,a6]
Generators	[-46655:1751268:125]	Generators of the group modulo torsion
j	-537367797/468512	j-invariant
L	3.4716475320636	L(r)(E,1)/r!
Ω	0.22819946666001	Real period
R	3.8033037312444	Regulator
r	1	Rank of the group of rational points
S	0.99999999999987	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3718t1 33462dg1	Quadratic twists by: -3 13

Hecke Eigenvalues for elliptic curve 33462ba1

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	+	-	-1	-2	-6	4	-8	1	0	9	11	-6	2	-8	-8	9	14	14	2	14	16

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Quadratic twists for elliptic curve 33462ba1

-3	13
3718t1	33462dg1

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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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