Cremona's table of elliptic curves

1034 = 2 · 11 · 47

Field	Data	Notes
Atkin-Lehner	2+ 11+ 47-	Signs for the Atkin-Lehner involutions
Class	1034a	Isogeny class
Conductor	1034	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-2068 = -1 · 22 · 11 · 47	Discriminant
Eigenvalues	2+ -2 -2 -5 11+ -3 -8 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-12,14]	[a1,a2,a3,a4,a6]
Generators	[12:-47:1] [-1:5:1]	Generators of the group modulo torsion
j	-169112377/2068	j-invariant
L	1.4721670735457	L(r)(E,1)/r!
Ω	4.6656082583932	Real period
R	0.15776796850618	Regulator
r	2	Rank of the group of rational points
S	1.0000000000007	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8272p1 33088r1 9306o1 25850i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1034a1

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	-2	-5	+	-3	-8	-4	3	-6	-1	1	-5	-6	-	-11	6	-2	13	-8	-6	17	-7	-3	-7

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Quadratic twists for elliptic curve 1034a1

-4	8	-3	5	-7	-11	-47
8272p1	33088r1	9306o1	25850i1	50666c1	11374l1	48598e1

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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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