Cremona's table of elliptic curves

17340 = 2² · 3 · 5 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 17+	Signs for the Atkin-Lehner involutions
Class	17340h	Isogeny class
Conductor	17340	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-2462032038000 = -1 · 24 · 3 · 53 · 177	Discriminant
Eigenvalues	2- 3+ 5- -5 -3  2 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2088410,-1160944683]	[a1,a2,a3,a4,a6]
Generators	[1723:18785:1]	Generators of the group modulo torsion
j	-2608300961238784/6375	j-invariant
L	3.2439785934508	L(r)(E,1)/r!
Ω	0.062793631581847	Real period
R	4.3050790764008	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69360dv2 52020y2 86700bo2 1020g2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 17340h2

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
-	+	-	-5	-3	2	+	-7	6	3	-2	-11	3	8	-9	9	12	10	8	-12	7	10	-12	-12	-2

---

Quadratic twists for elliptic curve 17340h2

-4	-3	5	17
69360dv2	52020y2	86700bo2	1020g2

---

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