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	1768b	Isogeny class
Conductor	1768	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	642638637056 = 211 · 13 · 176	Discriminant
Eigenvalues	2- -2  2  2  4 13+ 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2192,7840]	[a1,a2,a3,a4,a6]
j	569001644066/313788397	j-invariant
L	1.5825149739618	L(r)(E,1)/r!
Ω	0.79125748698091	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3536a2 14144g2 15912f2 44200i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1768b2

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	4	+	+	4	4	0	2	2	-4	-4	0	-6	-12	0	12	10	16	0	-4	14	8

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Quadratic twists for elliptic curve 1768b2

-4	8	-3	5	-7	13	17
3536a2	14144g2	15912f2	44200i2	86632bb2	22984b2	30056j2

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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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