Cremona's table of elliptic curves

48672 = 2⁵ · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 13+	Signs for the Atkin-Lehner involutions
Class	48672r	Isogeny class
Conductor	48672	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	43238323335168 = 212 · 37 · 136	Discriminant
Eigenvalues	2+ 3-  2  4  4 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-26364,1616992]	[a1,a2,a3,a4,a6]
j	140608/3	j-invariant
L	5.1296215281305	L(r)(E,1)/r!
Ω	0.64120269099388	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	48672bs3 97344ch1 16224v2 288b3	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 48672r3

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	4	+	6	4	0	-2	-4	2	2	4	8	-10	-4	6	-4	-16	6	4	12	10	14

---

Quadratic twists for elliptic curve 48672r3

-4	8	-3	13
48672bs3	97344ch1	16224v2	288b3

---

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