Elliptic curve isogeny class with LMFDB label 62400.er (Cremona label 62400cx)

• Label: 62400.er
• Number of curves: $4$
• Conductor: $62400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 62400.er have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 62400.er do not have complex multiplication.

Modular form 62400.2.a.er

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 62400.er

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
62400.er1	62400cx4	\([0, 1, 0, -1913633, -967699137]\)	\(189208196468929/10860320250\)	\(44483871744000000000\)	\([2]\)	\(1327104\)	\(2.5243\)
62400.er2	62400cx2	\([0, 1, 0, -329633, 72412863]\)	\(967068262369/4928040\)	\(20185251840000000\)	\([2]\)	\(442368\)	\(1.9750\)
62400.er3	62400cx1	\([0, 1, 0, -9633, 2332863]\)	\(-24137569/561600\)	\(-2300313600000000\)	\([2]\)	\(221184\)	\(1.6284\)	\(\Gamma_0(N)\)-optimal
62400.er4	62400cx3	\([0, 1, 0, 86367, -61699137]\)	\(17394111071/411937500\)	\(-1687296000000000000\)	\([2]\)	\(663552\)	\(2.1777\)