Cremona's table of elliptic curves

6118 = 2 · 7 · 19 · 23

Field	Data	Notes
Atkin-Lehner	2- 7+ 19+ 23-	Signs for the Atkin-Lehner involutions
Class	6118i	Isogeny class
Conductor	6118	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	10752	Modular degree for the optimal curve
Δ	-4292763123712 = -1 · 216 · 73 · 192 · 232	Discriminant
Eigenvalues	2- -2  0 7+  4  2 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,617,99561]	[a1,a2,a3,a4,a6]
Generators	[-10:309:1]	Generators of the group modulo torsion
j	25973783183375/4292763123712	j-invariant
L	4.2232398312739	L(r)(E,1)/r!
Ω	0.59960395380509	Real period
R	0.44021138916709	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	48944y1 55062f1 42826v1 116242f1	Quadratic twists by: -4 -3 -7 -19

Hecke Eigenvalues for elliptic curve 6118i1

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	-4	+	-	-6	2	-10	2	-4	2	2	10	4	-4	-12	14	0	0	0	-4

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Quadratic twists for elliptic curve 6118i1

-4	-3	-7	-19
48944y1	55062f1	42826v1	116242f1

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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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