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	17424a	Isogeny class
Conductor	17424	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	33792	Modular degree for the optimal curve
Δ	65192537760768 = 210 · 33 · 119	Discriminant
Eigenvalues	2+ 3+  2  2 11+ -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-11979,-322102]	[a1,a2,a3,a4,a6]
Generators	[-29:30:1]	Generators of the group modulo torsion
j	2916	j-invariant
L	6.2592160528354	L(r)(E,1)/r!
Ω	0.46907650329047	Real period
R	3.3359249551664	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	8712a1 69696dw1 17424c1 17424b1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424a1

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

---

Quadratic twists for elliptic curve 17424a1

-4	8	-3	-11
8712a1	69696dw1	17424c1	17424b1

---

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