Cremona's table of elliptic curves

1775 = 5² · 71

Field	Data	Notes
Atkin-Lehner	5- 71-	Signs for the Atkin-Lehner involutions
Class	1775b	Isogeny class
Conductor	1775	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	560	Modular degree for the optimal curve
Δ	-138671875 = -1 · 59 · 71	Discriminant
Eigenvalues	2  0 5- -3  2 -1  2 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-125,781]	[a1,a2,a3,a4,a6]
Generators	[50:121:8]	Generators of the group modulo torsion
j	-110592/71	j-invariant
L	4.9097878176645	L(r)(E,1)/r!
Ω	1.7014571539257	Real period
R	1.4428185294988	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	28400w1 113600bq1 15975u1 1775c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1775b1

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 1775b1

-4	8	-3	5	-7	-71
28400w1	113600bq1	15975u1	1775c1	86975bd1	126025h1

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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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