Elliptic curve isogeny class with Cremona label 243360cb (LMFDB label 243360.cb)

• Label: 243360cb
• Number of curves: $2$
• Conductor: $243360$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 243360cb have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 243360cb do not have complex multiplication.

Modular form 243360.2.a.cb

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 243360cb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
243360.cb2	243360cb1	\([0, 0, 0, 41067, -10202868]\)	\(1259712/8125\)	\(-49403162404440000\)	\([2]\)	\(1548288\)	\(1.8850\)	\(\Gamma_0(N)\)-optimal
243360.cb1	243360cb2	\([0, 0, 0, -529308, -134772768]\)	\(42144192/4225\)	\(1644137244819763200\)	\([2]\)	\(3096576\)	\(2.2316\)