Elliptic curve isogeny class with LMFDB label 5577.a (Cremona label 5577d)

• Label: 5577.a
• Number of curves: $4$
• Conductor: $5577$
• CM: no
• Rank: $1$

Elliptic curves in class 5577.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5577.a1	5577d3	\([1, 1, 1, -24762, 1487988]\)	\(347873904937/395307\)	\(1908071385363\)	\([2]\)	\(13824\)	\(1.2698\)
5577.a2	5577d2	\([1, 1, 1, -1947, 9576]\)	\(169112377/88209\)	\(425767995081\)	\([2, 2]\)	\(6912\)	\(0.92327\)
5577.a3	5577d1	\([1, 1, 1, -1102, -14422]\)	\(30664297/297\)	\(1433562273\)	\([2]\)	\(3456\)	\(0.57670\)	\(\Gamma_0(N)\)-optimal
5577.a4	5577d4	\([1, 1, 1, 7348, 83936]\)	\(9090072503/5845851\)	\(-28216806219459\)	\([2]\)	\(13824\)	\(1.2698\)

Rank

The elliptic curves in class 5577.a have rank \(1\).

Complex multiplication

The elliptic curves in class 5577.a do not have complex multiplication.

Modular form 5577.2.a.a

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.