Cremona's table of elliptic curves

17052 = 2² · 3 · 7² · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 29+	Signs for the Atkin-Lehner involutions
Class	17052i	Isogeny class
Conductor	17052	Conductor
∏ cp	162	Product of Tamagawa factors cp
deg	136080	Modular degree for the optimal curve
Δ	-24429330986957568 = -1 · 28 · 39 · 78 · 292	Discriminant
Eigenvalues	2- 3-  0 7+  0  5  6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-86893,12370511]	[a1,a2,a3,a4,a6]
Generators	[-151:4698:1]	Generators of the group modulo torsion
j	-49165312000/16553403	j-invariant
L	6.4377929690338	L(r)(E,1)/r!
Ω	0.35706721552668	Real period
R	1.0016466071207	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	68208ba1 51156h1 17052b1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 17052i1

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	+	0	5	6	-7	6	+	-7	-7	-6	-7	-12	-12	6	2	5	12	-13	-1	6	0	-10

---

Quadratic twists for elliptic curve 17052i1

-4	-3	-7
68208ba1	51156h1	17052b1

---

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