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	618a	Isogeny class
Conductor	618	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-4944 = -1 · 24 · 3 · 103	Discriminant
Eigenvalues	2+ 3+ -1 -2  6 -1  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,2,4]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	357911/4944	j-invariant
L	1.3562810365111	L(r)(E,1)/r!
Ω	3.2025259469404	Real period
R	0.21175176391729	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	4944k1 19776l1 1854f1 15450bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 618a1

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
+	+	-1	-2	6	-1	0	-8	3	-6	-5	6	4	-9	-10	-6	-5	15	-15	0	-16	6	-9	2	1

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Quadratic twists for elliptic curve 618a1

-4	8	-3	5	-7	-11	13	-103
4944k1	19776l1	1854f1	15450bf1	30282o1	74778x1	104442x1	63654c1

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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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