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	1768a	Isogeny class
Conductor	1768	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3847168 = 210 · 13 · 172	Discriminant
Eigenvalues	2+  0  4  2 -2 13+ 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-283,1830]	[a1,a2,a3,a4,a6]
j	2447840196/3757	j-invariant
L	2.480061218229	L(r)(E,1)/r!
Ω	2.480061218229	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3536c2 14144l2 15912o2 44200o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1768a2

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

---

Quadratic twists for elliptic curve 1768a2

-4	8	-3	5	-7	13	17
3536c2	14144l2	15912o2	44200o2	86632h2	22984g2	30056c2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations