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	17340f	Isogeny class
Conductor	17340	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-3386718750000 = -1 · 24 · 3 · 512 · 172	Discriminant
Eigenvalues	2- 3+ 5-  1  0  5 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,295,88422]	[a1,a2,a3,a4,a6]
Generators	[-26:250:1]	Generators of the group modulo torsion
j	611926016/732421875	j-invariant
L	4.9414437028362	L(r)(E,1)/r!
Ω	0.62051022233955	Real period
R	0.66362641647347	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	69360dq2 52020q2 86700bh2 17340o2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 17340f2

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	0	5	+	-1	-6	0	-5	1	0	5	-12	12	12	1	-13	-6	-2	-8	-6	-6	-17

---

Quadratic twists for elliptic curve 17340f2

-4	-3	5	17
69360dq2	52020q2	86700bh2	17340o2

---

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