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	4368b	Isogeny class
Conductor	4368	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	30820608 = 28 · 33 · 73 · 13	Discriminant
Eigenvalues	2+ 3+  2 7+ -4 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-40132,3107872]	[a1,a2,a3,a4,a6]
Generators	[3432:5680:27]	Generators of the group modulo torsion
j	27923315228972368/120393	j-invariant
L	3.3779180509927	L(r)(E,1)/r!
Ω	1.404899275261	Real period
R	4.8087690135154	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	2184l1 17472ct1 13104n1 109200cc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4368b1

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	8	-6	-8	2	2	4	12	-6	-12	-6	0	-16	-2	0	4	2	-10

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Quadratic twists for elliptic curve 4368b1

-4	8	-3	5	-7	13
2184l1	17472ct1	13104n1	109200cc1	30576bd1	56784f1

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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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