Cremona's table of elliptic curves

618 = 2 · 3 · 103

Field	Data	Notes
Atkin-Lehner	2- 3- 103-	Signs for the Atkin-Lehner involutions
Class	618g	Isogeny class
Conductor	618	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	224	Modular degree for the optimal curve
Δ	-79104 = -1 · 28 · 3 · 103	Discriminant
Eigenvalues	2- 3-  3 -2 -2  3  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1484,-22128]	[a1,a2,a3,a4,a6]
j	-361446235206337/79104	j-invariant
L	3.0768019408855	L(r)(E,1)/r!
Ω	0.38460024261068	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4944e1 19776j1 1854d1 15450c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 618g1

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
-	-	3	-2	-2	3	0	0	-3	-2	-3	2	0	-3	-10	10	9	-5	-5	8	-4	-2	-3	10	-7

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Quadratic twists for elliptic curve 618g1

-4	8	-3	5	-7	-11	13	-103
4944e1	19776j1	1854d1	15450c1	30282z1	74778u1	104442r1	63654g1

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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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