Cremona's table of elliptic curves

6942 = 2 · 3 · 13 · 89

Field	Data	Notes
Atkin-Lehner	2- 3- 13- 89+	Signs for the Atkin-Lehner involutions
Class	6942n	Isogeny class
Conductor	6942	Conductor
∏ cp	486	Product of Tamagawa factors cp
deg	65664	Modular degree for the optimal curve
Δ	-1008907331567616 = -1 · 218 · 39 · 133 · 89	Discriminant
Eigenvalues	2- 3- -3 -1  3 13-  0 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-210177,37101321]	[a1,a2,a3,a4,a6]
j	-1026784744653907139473/1008907331567616	j-invariant
L	2.9453757579909	L(r)(E,1)/r!
Ω	0.49089595966515	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	9	Number of elements in the torsion subgroup
Twists	55536ba1 20826p1 90246k1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 6942n1

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
-	-	-3	-1	3	-	0	-7	-3	3	5	2	6	8	3	0	-12	8	14	9	2	-1	12	+	-10

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Quadratic twists for elliptic curve 6942n1

-4	-3	13
55536ba1	20826p1	90246k1

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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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