Cremona's table of elliptic curves

1120 = 2⁵ · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 5- 7+	Signs for the Atkin-Lehner involutions
Class	1120n	Isogeny class
Conductor	1120	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-143360 = -1 · 212 · 5 · 7	Discriminant
Eigenvalues	2- -3 5- 7+ -3  1 -1  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,8,16]	[a1,a2,a3,a4,a6]
Generators	[0:4:1]	Generators of the group modulo torsion
j	13824/35	j-invariant
L	1.706500509815	L(r)(E,1)/r!
Ω	2.282670275662	Real period
R	0.37379478937668	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	1120p1 2240r1 10080k1 5600i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1120n1

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	-	+	-3	1	-1	4	4	-9	6	-8	6	-8	-7	-8	4	10	-8	-12	-14	-5	-16	-14	-17

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Quadratic twists for elliptic curve 1120n1

-4	8	-3	5	-7
1120p1	2240r1	10080k1	5600i1	7840t1

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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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