Elliptic curve isogeny class with Cremona label 443760df (LMFDB label 443760.df)

• Label: 443760df
• Number of curves: $4$
• Conductor: $443760$
• CM: no
• Rank: $1$

Elliptic curves in class 443760df

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
443760.df3	443760df1	\([0, 1, 0, -2027120, -1110163500]\)	\(35578826569/51600\)	\(1336042837313126400\)	\([2]\)	\(8515584\)	\(2.3801\)	\(\Gamma_0(N)\)-optimal^*
443760.df2	443760df2	\([0, 1, 0, -2618800, -409851052]\)	\(76711450249/41602500\)	\(1077184537583708160000\)	\([2, 2]\)	\(17031168\)	\(2.7267\)	\(\Gamma_0(N)\)-optimal^*
443760.df1	443760df3	\([0, 1, 0, -24806800, 47223347348]\)	\(65202655558249/512820150\)	\(13278094733281842585600\)	\([2]\)	\(34062336\)	\(3.0732\)	\(\Gamma_0(N)\)-optimal^*
443760.df4	443760df4	\([0, 1, 0, 10102320, -3213585900]\)	\(4403686064471/2721093750\)	\(-70455383998934400000000\)	\([4]\)	\(34062336\)	\(3.0732\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 443760df1.

Rank

The elliptic curves in class 443760df have rank \(1\).

Complex multiplication

The elliptic curves in class 443760df do not have complex multiplication.

Modular form 443760.2.a.df

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.