Cremona's table of elliptic curves

17328 = 2⁴ · 3 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3- 19+	Signs for the Atkin-Lehner involutions
Class	17328bc	Isogeny class
Conductor	17328	Conductor
∏ cp	56	Product of Tamagawa factors cp
deg	53760	Modular degree for the optimal curve
Δ	15729303748608 = 220 · 37 · 193	Discriminant
Eigenvalues	2- 3-  2 -4  2  4  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-15472,710612]	[a1,a2,a3,a4,a6]
Generators	[-46:1152:1]	Generators of the group modulo torsion
j	14580432307/559872	j-invariant
L	6.6220251340033	L(r)(E,1)/r!
Ω	0.69233604871348	Real period
R	0.68319683218127	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	2166f1 69312ci1 51984cf1 17328q1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 17328bc1

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

---

Quadratic twists for elliptic curve 17328bc1

-4	8	-3	-19
2166f1	69312ci1	51984cf1	17328q1

---

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