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	4368s	Isogeny class
Conductor	4368	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	1375605504 = 28 · 310 · 7 · 13	Discriminant
Eigenvalues	2- 3+ -2 7-  0 13+ -4  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-404,-2436]	[a1,a2,a3,a4,a6]
Generators	[282:1287:8]	Generators of the group modulo torsion
j	28556329552/5373459	j-invariant
L	2.8132047788618	L(r)(E,1)/r!
Ω	1.0785386209192	Real period
R	5.2166973426767	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	1092e2 17472dc2 13104cc2 109200fg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4368s2

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

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Quadratic twists for elliptic curve 4368s2

-4	8	-3	5	-7	13
1092e2	17472dc2	13104cc2	109200fg2	30576cz2	56784bi2

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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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