Cremona's table of elliptic curves

1775 = 5² · 71

Field	Data	Notes
Atkin-Lehner	5- 71-	Signs for the Atkin-Lehner involutions
Class	1775c	Isogeny class
Conductor	1775	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	-8875 = -1 · 53 · 71	Discriminant
Eigenvalues	-2  0 5-  3  2  1 -2 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-5,6]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	-110592/71	j-invariant
L	1.6485516590422	L(r)(E,1)/r!
Ω	3.8045738569812	Real period
R	0.21665391723402	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	28400x1 113600bp1 15975t1 1775b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1775c1

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	-	3	2	1	-2	-5	0	-3	-8	-4	-2	-2	3	9	0	-8	-8	-	4	15	-12	-9	-7

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Quadratic twists for elliptic curve 1775c1

-4	8	-3	5	-7	-71
28400x1	113600bp1	15975t1	1775b1	86975be1	126025i1

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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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