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	1342a	Isogeny class
Conductor	1342	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	162382 = 2 · 113 · 61	Discriminant
Eigenvalues	2+  1 -2  4 11+ -3 -3  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-37,-86]	[a1,a2,a3,a4,a6]
Generators	[-4:2:1]	Generators of the group modulo torsion
j	5386984777/162382	j-invariant
L	2.2475277566845	L(r)(E,1)/r!
Ω	1.9456525336411	Real period
R	1.1551537172356	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	10736h1 42944k1 12078u1 33550p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1342a1

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	-2	4	+	-3	-3	0	-4	0	-3	3	0	1	-6	1	6	+	-8	-13	0	-2	-12	-6	11

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Quadratic twists for elliptic curve 1342a1

-4	8	-3	5	-7	-11	61
10736h1	42944k1	12078u1	33550p1	65758e1	14762h1	81862h1

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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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