Cremona's table of elliptic curves

1342 = 2 · 11 · 61

Field	Data	Notes
Atkin-Lehner	2- 11- 61+	Signs for the Atkin-Lehner involutions
Class	1342b	Isogeny class
Conductor	1342	Conductor
∏ cp	11	Product of Tamagawa factors cp
deg	176	Modular degree for the optimal curve
Δ	1374208 = 211 · 11 · 61	Discriminant
Eigenvalues	2- -1  0 -2 11-  1 -5  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-28,-3]	[a1,a2,a3,a4,a6]
Generators	[-3:9:1]	Generators of the group modulo torsion
j	2433138625/1374208	j-invariant
L	3.1617282877633	L(r)(E,1)/r!
Ω	2.3301844835636	Real period
R	0.12335068161751	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	10736e1 42944c1 12078f1 33550b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1342b1

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	0	-2	-	1	-5	4	-4	-6	-7	5	0	-11	-8	7	-4	+	16	-13	-6	4	-2	0	7

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Quadratic twists for elliptic curve 1342b1

-4	8	-3	5	-7	-11	61
10736e1	42944c1	12078f1	33550b1	65758ba1	14762e1	81862a1

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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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