Cremona's table of elliptic curves

1769 = 29 · 61

Field	Data	Notes
Atkin-Lehner	29- 61+	Signs for the Atkin-Lehner involutions
Class	1769a	Isogeny class
Conductor	1769	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1080	Modular degree for the optimal curve
Δ	-90751469 = -1 · 293 · 612	Discriminant
Eigenvalues	-1  1  3  4  1  1  4  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2544,-49603]	[a1,a2,a3,a4,a6]
j	-1820898350896897/90751469	j-invariant
L	2.0166909291115	L(r)(E,1)/r!
Ω	0.33611515485192	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	28304e1 113216d1 15921b1 44225c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1769a1

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
-1	1	3	4	1	1	4	8	-6	-	3	-4	-4	1	1	9	-6	+	-4	-2	-14	-15	-14	8	4

---

Quadratic twists for elliptic curve 1769a1

-4	8	-3	5	-7	29	61
28304e1	113216d1	15921b1	44225c1	86681i1	51301a1	107909a1

---

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