Cremona's table of elliptic curves

13872 = 2⁴ · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3+ 17+	Signs for the Atkin-Lehner involutions
Class	13872u	Isogeny class
Conductor	13872	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	6048	Modular degree for the optimal curve
Δ	-454557696 = -1 · 219 · 3 · 172	Discriminant
Eigenvalues	2- 3+  1  4 -3  6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,40,1008]	[a1,a2,a3,a4,a6]
j	5831/384	j-invariant
L	2.5434112935503	L(r)(E,1)/r!
Ω	1.2717056467751	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1734e1 55488dm1 41616ce1 13872bp1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872u1

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
-	+	1	4	-3	6	+	-4	6	7	-3	-8	-2	4	2	13	-9	10	6	-12	7	-5	-12	4	-3

---

Quadratic twists for elliptic curve 13872u1

-4	8	-3	17
1734e1	55488dm1	41616ce1	13872bp1

---

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