Cremona's table of elliptic curves

1763 = 41 · 43

Field	Data	Notes
Atkin-Lehner	41+ 43-	Signs for the Atkin-Lehner involutions
Class	1763b	Isogeny class
Conductor	1763	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-1763 = -1 · 41 · 43	Discriminant
Eigenvalues	1  1 -4  3  0  0  4  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3,-3]	[a1,a2,a3,a4,a6]
j	-1771561/1763	j-invariant
L	1.8212337024689	L(r)(E,1)/r!
Ω	1.8212337024689	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	28208f1 112832e1 15867g1 44075a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1763b1

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
1	1	-4	3	0	0	4	4	1	-2	9	4	+	-	2	6	5	8	4	-7	-8	-4	1	1	2

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Quadratic twists for elliptic curve 1763b1

-4	8	-3	5	-7	41	-43
28208f1	112832e1	15867g1	44075a1	86387f1	72283c1	75809h1

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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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