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	1768d	Isogeny class
Conductor	1768	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	35921969408 = 28 · 134 · 173	Discriminant
Eigenvalues	2- -2  2  2 -2 13+ 17- -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1412,-18752]	[a1,a2,a3,a4,a6]
Generators	[-18:34:1]	Generators of the group modulo torsion
j	1217013440848/140320193	j-invariant
L	2.4449559243797	L(r)(E,1)/r!
Ω	0.78463316617772	Real period
R	0.51934161290728	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	3536d1 14144n1 15912c1 44200g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1768d1

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	2	2	-2	+	-	-8	-2	6	-10	2	-10	8	0	6	0	6	-12	-2	-2	6	-16	-10	-10

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Quadratic twists for elliptic curve 1768d1

-4	8	-3	5	-7	13	17
3536d1	14144n1	15912c1	44200g1	86632x1	22984f1	30056i1

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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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