Cremona's table of elliptic curves

17472 = 2⁶ · 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	17472cf	Isogeny class
Conductor	17472	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	8192	Modular degree for the optimal curve
Δ	-4299230208 = -1 · 210 · 3 · 72 · 134	Discriminant
Eigenvalues	2- 3+ -2 7-  0 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-29,3165]	[a1,a2,a3,a4,a6]
Generators	[1:56:1]	Generators of the group modulo torsion
j	-2725888/4198467	j-invariant
L	3.2986055462532	L(r)(E,1)/r!
Ω	1.1137650417401	Real period
R	1.4808354646773	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	17472w1 4368m1 52416fy1 122304ie1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472cf1

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
-	+	-2	-	0	+	-6	-4	0	2	8	-6	6	4	12	2	0	2	-12	-4	10	16	0	-2	2

---

Quadratic twists for elliptic curve 17472cf1

-4	8	-3	-7
17472w1	4368m1	52416fy1	122304ie1

---

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