Cremona's table of elliptic curves

1760 = 2⁵ · 5 · 11

Field	Data	Notes
Atkin-Lehner	2+ 5- 11-	Signs for the Atkin-Lehner involutions
Class	1760h	Isogeny class
Conductor	1760	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	38720 = 26 · 5 · 112	Discriminant
Eigenvalues	2+ -2 5- -4 11-  4  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-10,-12]	[a1,a2,a3,a4,a6]
Generators	[-2:2:1]	Generators of the group modulo torsion
j	1906624/605	j-invariant
L	2.0832839505604	L(r)(E,1)/r!
Ω	2.7294415782849	Real period
R	0.76326379986834	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1760e1 3520s2 15840w1 8800z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1760h1

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	-	-4	-	4	4	-4	6	-10	4	2	-10	-8	-6	2	-4	-10	-2	0	12	8	0	-10	-2

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Quadratic twists for elliptic curve 1760h1

-4	8	-3	5	-7	-11
1760e1	3520s2	15840w1	8800z1	86240j1	19360bb1

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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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