Elliptic curve isogeny class with Cremona label 174570cl (LMFDB label 174570.t)

• Label: 174570cl
• Number of curves: $4$
• Conductor: $174570$
• CM: no
• Rank: $1$

Elliptic curves in class 174570cl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
174570.t3	174570cl1	\([1, 1, 0, -737172, 243305856]\)	\(299270638153369/1069200\)	\(158279972518800\)	\([2]\)	\(1971200\)	\(1.9426\)	\(\Gamma_0(N)\)-optimal
174570.t2	174570cl2	\([1, 1, 0, -747752, 235948524]\)	\(312341975961049/17862322500\)	\(2644264790892202500\)	\([2, 2]\)	\(3942400\)	\(2.2892\)
174570.t4	174570cl3	\([1, 1, 0, 537718, 964295826]\)	\(116149984977671/2779502343750\)	\(-411466100434614843750\)	\([2]\)	\(7884800\)	\(2.6357\)
174570.t1	174570cl4	\([1, 1, 0, -2202502, -963056426]\)	\(7981893677157049/1917731420550\)	\(283893075704352118950\)	\([2]\)	\(7884800\)	\(2.6357\)

Rank

The elliptic curves in class 174570cl have rank \(1\).

Complex multiplication

The elliptic curves in class 174570cl do not have complex multiplication.

Modular form 174570.2.a.cl

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.