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

• Label: 324480em
• Number of curves: $2$
• Conductor: $324480$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 324480em have rank \(1\).

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
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 324480.2.a.em

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 324480em

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
324480.em1	324480em1	\([0, 1, 0, -14981906, 17188288794]\)	\(601942297084171232/141650616290625\)	\(87516220104593326800000\)	\([2]\)	\(30105600\)	\(3.1139\)	\(\Gamma_0(N)\)-optimal
324480.em2	324480em2	\([0, 1, 0, 34914499, 107410968315]\)	\(59519748892520576/97453916015625\)	\(-7706893335092640000000000\)	\([2]\)	\(60211200\)	\(3.4604\)