Elliptic curve isogeny class with Cremona label 324480bo (LMFDB label 324480.bo)

• Label: 324480bo
• Number of curves: $2$
• Conductor: $324480$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 324480bo have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 324480bo do not have complex multiplication.

Modular form 324480.2.a.bo

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 324480bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
324480.bo2	324480bo1	\([0, -1, 0, -22026, -830610]\)	\(1912847072/616005\)	\(380587325189760\)	\([2]\)	\(1290240\)	\(1.5012\)	\(\Gamma_0(N)\)-optimal
324480.bo1	324480bo2	\([0, -1, 0, -318621, -69106779]\)	\(45234335104/8775\)	\(693948399206400\)	\([2]\)	\(2580480\)	\(1.8478\)