Elliptic curve isogeny class with Cremona label 32448u (LMFDB label 32448.bt)

• Label: 32448u
• Number of curves: $2$
• Conductor: $32448$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 32448u have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 32448u do not have complex multiplication.

Modular form 32448.2.a.u

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 32448u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
32448.bt2	32448u1	\([0, -1, 0, -1421, 20253]\)	\(141150208/6561\)	\(14760465408\)	\([2]\)	\(36864\)	\(0.71250\)	\(\Gamma_0(N)\)-optimal
32448.bt1	32448u2	\([0, -1, 0, -22481, 1304913]\)	\(34909201168/81\)	\(2915647488\)	\([2]\)	\(73728\)	\(1.0591\)