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	618c	Isogeny class
Conductor	618	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	-5562 = -1 · 2 · 33 · 103	Discriminant
Eigenvalues	2+ 3-  0 -4 -3  2 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-21,34]	[a1,a2,a3,a4,a6]
Generators	[-4:9:1]	Generators of the group modulo torsion
j	-955671625/5562	j-invariant
L	1.7322241585865	L(r)(E,1)/r!
Ω	4.3034232575024	Real period
R	1.2075671308184	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	4944b1 19776e1 1854h1 15450w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 618c1

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
+	-	0	-4	-3	2	-6	-1	-9	9	-1	5	0	2	-6	-12	-12	8	14	-12	-16	2	12	3	-1

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Quadratic twists for elliptic curve 618c1

-4	8	-3	5	-7	-11	13	-103
4944b1	19776e1	1854h1	15450w1	30282b1	74778bq1	104442bk1	63654a1

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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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