Cremona's table of elliptic curves

4368 = 2⁴ · 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 13-	Signs for the Atkin-Lehner involutions
Class	4368k	Isogeny class
Conductor	4368	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	1105112825736192 = 210 · 33 · 72 · 138	Discriminant
Eigenvalues	2+ 3- -2 7+  4 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-37744,-2338108]	[a1,a2,a3,a4,a6]
Generators	[-136:546:1]	Generators of the group modulo torsion
j	5807363790481348/1079211743883	j-invariant
L	3.9019988077212	L(r)(E,1)/r!
Ω	0.34691814013638	Real period
R	0.46865028041236	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2184j4 17472br3 13104w4 109200q3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4368k3

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
+	-	-2	+	4	-	-6	-4	0	6	0	6	-6	-4	0	-2	-4	-2	-4	0	-6	-8	-12	10	-14

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Quadratic twists for elliptic curve 4368k3

-4	8	-3	5	-7	13
2184j4	17472br3	13104w4	109200q3	30576d3	56784u3

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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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