Cremona's table of elliptic curves

32448 = 2⁶ · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 13+	Signs for the Atkin-Lehner involutions
Class	32448bi	Isogeny class
Conductor	32448	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	129024	Modular degree for the optimal curve
Δ	238219473915072 = 26 · 33 · 1310	Discriminant
Eigenvalues	2+ 3- -2  0  4 13+ -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-15604,101882]	[a1,a2,a3,a4,a6]
j	1360251712/771147	j-invariant
L	1.4363176639797	L(r)(E,1)/r!
Ω	0.4787725546605	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	32448f1 16224c3 97344bq1 2496h1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448bi1

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

---

Quadratic twists for elliptic curve 32448bi1

-4	8	-3	13
32448f1	16224c3	97344bq1	2496h1

---

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