Elliptic curve isogeny class with LMFDB label 77658.ba (Cremona label 77658x)

• Label: 77658.ba
• Number of curves: $4$
• Conductor: $77658$
• CM: no
• Rank: $1$

Elliptic curves in class 77658.ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
77658.ba1	77658x4	\([1, 1, 1, -1713137, -863480797]\)	\(87960822051817/33450732\)	\(211454221226801868\)	\([2]\)	\(1419264\)	\(2.2906\)
77658.ba2	77658x3	\([1, 1, 1, -899577, 321565491]\)	\(12735853007977/287179284\)	\(1815364514315876916\)	\([2]\)	\(1419264\)	\(2.2906\)
77658.ba3	77658x2	\([1, 1, 1, -122997, -9257589]\)	\(32553430057/13046544\)	\(82471941158752656\)	\([2, 2]\)	\(709632\)	\(1.9440\)
77658.ba4	77658x1	\([1, 1, 1, 24923, -1033237]\)	\(270840023/231168\)	\(-1461296853311232\)	\([4]\)	\(354816\)	\(1.5974\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 77658.ba have rank \(1\).

Complex multiplication

The elliptic curves in class 77658.ba do not have complex multiplication.

Modular form 77658.2.a.ba

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.