Cremona's table of elliptic curves

1763 = 41 · 43

Field	Data	Notes
Atkin-Lehner	41+ 43+	Signs for the Atkin-Lehner involutions
Class	1763a	Isogeny class
Conductor	1763	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	52	Modular degree for the optimal curve
Δ	-1763 = -1 · 41 · 43	Discriminant
Eigenvalues	0  1 -2  0  2  6  4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,1,-2]	[a1,a2,a3,a4,a6]
Generators	[2:3:1]	Generators of the group modulo torsion
j	32768/1763	j-invariant
L	2.6314123250307	L(r)(E,1)/r!
Ω	2.2528108121397	Real period
R	1.1680573933909	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	28208g1 112832h1 15867d1 44075c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1763a1

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
0	1	-2	0	2	6	4	-5	-3	-3	0	-2	+	+	2	-10	-9	-14	2	5	-2	-2	-4	-7	14

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Quadratic twists for elliptic curve 1763a1

-4	8	-3	5	-7	41	-43
28208g1	112832h1	15867d1	44075c1	86387c1	72283a1	75809e1

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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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