Cremona's table of elliptic curves

1387 = 19 · 73

Field	Data	Notes
Atkin-Lehner	19+ 73+	Signs for the Atkin-Lehner involutions
Class	1387a	Isogeny class
Conductor	1387	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	60	Modular degree for the optimal curve
Δ	-1387 = -1 · 19 · 73	Discriminant
Eigenvalues	-2  0  2  0 -2  5 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,1,-2]	[a1,a2,a3,a4,a6]
Generators	[1:0:1]	Generators of the group modulo torsion
j	110592/1387	j-invariant
L	1.5867246794725	L(r)(E,1)/r!
Ω	2.3588146291083	Real period
R	0.67267883617984	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	22192c1 88768e1 12483g1 34675a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1387a1

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	2	0	-2	5	-2	+	-5	-3	0	-8	-6	6	2	2	-7	7	4	10	+	-8	14	-16	-10

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Quadratic twists for elliptic curve 1387a1

-4	8	-3	5	-7	-19	73
22192c1	88768e1	12483g1	34675a1	67963i1	26353a1	101251a1

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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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