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	17424bb	Isogeny class
Conductor	17424	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-836352 = -1 · 28 · 33 · 112	Discriminant
Eigenvalues	2- 3+  0 -1 11- -2  0 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,0,44]	[a1,a2,a3,a4,a6]
Generators	[-2:6:1]	Generators of the group modulo torsion
j	0	j-invariant
L	4.6265700189652	L(r)(E,1)/r!
Ω	2.2388082346945	Real period
R	0.51663312954499	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	4356a1 69696ed1 17424bb2 17424ba1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424bb1

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	-1	-	-2	0	-1	0	0	7	-1	0	8	0	0	0	13	-5	0	7	17	0	0	-19

---

Quadratic twists for elliptic curve 17424bb1

-4	8	-3	-11
4356a1	69696ed1	17424bb2	17424ba1

---

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