Cremona's table of elliptic curves

17424 = 2⁴ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3- 11-	Signs for the Atkin-Lehner involutions
Class	17424z	Isogeny class
Conductor	17424	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-1.5307227186926E+21	Discriminant
Eigenvalues	2+ 3- -4 -2 11-  0 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8686227,10031786930]	[a1,a2,a3,a4,a6]
Generators	[583:71874:1]	Generators of the group modulo torsion
j	-27403349188178/578739249	j-invariant
L	2.8417450963223	L(r)(E,1)/r!
Ω	0.15070267458456	Real period
R	2.3570791826987	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	8712n2 69696hb2 5808g2 1584e2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424z2

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	-2	-	0	-6	4	-6	6	0	6	-10	-8	6	12	-8	-4	12	10	-2	2	-12	6	14

---

Quadratic twists for elliptic curve 17424z2

-4	8	-3	-11
8712n2	69696hb2	5808g2	1584e2

---

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