Cremona's table of elliptic curves

2618 = 2 · 7 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2+ 7+ 11+ 17+	Signs for the Atkin-Lehner involutions
Class	2618a	Isogeny class
Conductor	2618	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	228480	Modular degree for the optimal curve
Δ	-1.4855248670547E+21	Discriminant
Eigenvalues	2+  0  3 7+ 11+ -5 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-18139238,-29788828748]	[a1,a2,a3,a4,a6]
Generators	[116692465710459280103244:-27995070447560262047442470:2024539071435303877]	Generators of the group modulo torsion
j	-660056090712855266747143737/1485524867054684667904	j-invariant
L	2.6575432190886	L(r)(E,1)/r!
Ω	0.036572633678175	Real period
R	36.332401468184	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	20944m1 83776h1 23562bd1 65450bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2618a1

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	3	+	+	-5	+	8	-3	5	-2	-4	4	-1	-12	-1	-5	0	-12	-1	-10	-14	-6	-6	-14

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Quadratic twists for elliptic curve 2618a1

-4	8	-3	5	-7	-11	17
20944m1	83776h1	23562bd1	65450bb1	18326j1	28798bb1	44506m1

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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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