Cremona's table of elliptic curves

17850 = 2 · 3 · 5² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7+ 17+	Signs for the Atkin-Lehner involutions
Class	17850a	Isogeny class
Conductor	17850	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	3.6306142575413E+21	Discriminant
Eigenvalues	2+ 3+ 5+ 7+ -4  6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-14985400,-22145288000]	[a1,a2,a3,a4,a6]
Generators	[-122785942:-692898955:54872]	Generators of the group modulo torsion
j	23818189767728437646209/232359312482640000	j-invariant
L	2.7933956612919	L(r)(E,1)/r!
Ω	0.076778258492549	Real period
R	9.0956597484007	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53550ds3 3570x3 124950df3	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 17850a3

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

---

Quadratic twists for elliptic curve 17850a3

-3	5	-7
53550ds3	3570x3	124950df3

---

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