Cremona's table of elliptic curves

1768 = 2³ · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 13+ 17-	Signs for the Atkin-Lehner involutions
Class	1768c	Isogeny class
Conductor	1768	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	60112 = 24 · 13 · 172	Discriminant
Eigenvalues	2-  0  0 -2  6 13+ 17- -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-10,-3]	[a1,a2,a3,a4,a6]
Generators	[-2:3:1]	Generators of the group modulo torsion
j	6912000/3757	j-invariant
L	2.8050900672954	L(r)(E,1)/r!
Ω	2.8637921373593	Real period
R	0.97950197945649	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	3536b1 14144j1 15912b1 44200e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1768c1

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	0	-2	6	+	-	-8	4	2	-2	-4	12	-12	-8	-6	0	6	-8	-14	-4	-16	-4	6	0

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Quadratic twists for elliptic curve 1768c1

-4	8	-3	5	-7	13	17
3536b1	14144j1	15912b1	44200e1	86632w1	22984c1	30056f1

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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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