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	17424bd	Isogeny class
Conductor	17424	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	6435169410679308288 = 224 · 39 · 117	Discriminant
Eigenvalues	2- 3+  0  2 11- -2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1127115,-444109446]	[a1,a2,a3,a4,a6]
Generators	[-3541961:-3243520:6859]	Generators of the group modulo torsion
j	1108717875/45056	j-invariant
L	5.1562167532118	L(r)(E,1)/r!
Ω	0.14689085913607	Real period
R	8.7755915915015	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	2178g3 69696ef3 17424bc1 1584h3	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424bd3

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

---

Quadratic twists for elliptic curve 17424bd3

-4	8	-3	-11
2178g3	69696ef3	17424bc1	1584h3

---

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