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

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

Elliptic curves in class 443760.df

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

Rank

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

Complex multiplication

The elliptic curves in class 443760.df 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 LMFDB 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 LMFDB labels.