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	2618c	Isogeny class
Conductor	2618	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	31680	Modular degree for the optimal curve
Δ	-298276259387932672 = -1 · 222 · 75 · 114 · 172	Discriminant
Eigenvalues	2+  2  0 7- 11+ -4 17- -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,18590,-26250636]	[a1,a2,a3,a4,a6]
Generators	[18708:2549622:1]	Generators of the group modulo torsion
j	710436683544572375/298276259387932672	j-invariant
L	3.2841063365578	L(r)(E,1)/r!
Ω	0.14389365303155	Real period
R	2.2823149370166	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20944h1 83776r1 23562bi1 65450v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2618c1

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	0	-	+	-4	-	-2	-8	-2	0	-2	10	-8	0	-10	-6	4	-12	16	6	8	-2	10	-18

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Quadratic twists for elliptic curve 2618c1

-4	8	-3	5	-7	-11	17
20944h1	83776r1	23562bi1	65450v1	18326h1	28798r1	44506d1

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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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