Cremona's table of elliptic curves

5618 = 2 · 53²

Field	Data	Notes
Atkin-Lehner	2+ 53+	Signs for the Atkin-Lehner involutions
Class	5618c	Isogeny class
Conductor	5618	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-6599527183604266 = -1 · 2 · 539	Discriminant
Eigenvalues	2+  2 -3  2 -3 -4  3  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-25339,-4216161]	[a1,a2,a3,a4,a6]
Generators	[437835:55535519:27]	Generators of the group modulo torsion
j	-81182737/297754	j-invariant
L	3.4320703479612	L(r)(E,1)/r!
Ω	0.17333909863929	Real period
R	4.9499368216734	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	44944g2 50562bd2 106a2	Quadratic twists by: -4 -3 53

Hecke Eigenvalues for elliptic curve 5618c2

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	-3	2	-3	-4	3	4	9	6	-5	-10	-6	-1	0	+	15	10	4	-12	-8	-11	6	9	-13

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Quadratic twists for elliptic curve 5618c2

-4	-3	53
44944g2	50562bd2	106a2

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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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