Elliptic curve isogeny class with Cremona label 13248z (LMFDB label 13248.i)

• Label: 13248z
• Number of curves: $2$
• Conductor: $13248$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 13248z have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(23\)	\(1 + T\)

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.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 13248z do not have complex multiplication.

Modular form 13248.2.a.z

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 13248z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13248.i2	13248z1	\([0, 0, 0, -96, -360]\)	\(3538944/23\)	\(635904\)	\([2]\)	\(1536\)	\(-0.050348\)	\(\Gamma_0(N)\)-optimal
13248.i1	13248z2	\([0, 0, 0, -156, 144]\)	\(949104/529\)	\(234012672\)	\([2]\)	\(3072\)	\(0.29623\)