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	13872k	Isogeny class
Conductor	13872	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-1157194450372608 = -1 · 211 · 34 · 178	Discriminant
Eigenvalues	2+ 3-  0  2  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2408,1636500]	[a1,a2,a3,a4,a6]
j	-31250/23409	j-invariant
L	3.155027137909	L(r)(E,1)/r!
Ω	0.39437839223863	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6936c2 55488cc2 41616r2 816a2	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872k2

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

---

Quadratic twists for elliptic curve 13872k2

-4	8	-3	17
6936c2	55488cc2	41616r2	816a2

---

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