Cremona's table of elliptic curves

1368 = 2³ · 3² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 19-	Signs for the Atkin-Lehner involutions
Class	1368b	Isogeny class
Conductor	1368	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	95738112 = 28 · 39 · 19	Discriminant
Eigenvalues	2+ 3+  0  0  2 -2  4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-135,378]	[a1,a2,a3,a4,a6]
j	54000/19	j-invariant
L	1.7426827318272	L(r)(E,1)/r!
Ω	1.7426827318272	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2736b1 10944b1 1368e1 34200ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1368b1

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	0	2	-2	4	-	2	6	4	2	-2	4	10	6	4	2	4	4	-6	8	-2	6	-10

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Quadratic twists for elliptic curve 1368b1

-4	8	-3	5	-7	-19
2736b1	10944b1	1368e1	34200ca1	67032a1	25992r1

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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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