Elliptic curve isogeny class with Cremona label 70560ee (LMFDB label 70560.cl)

• Label: 70560ee
• Number of curves: $4$
• Conductor: $70560$
• CM: no
• Rank: $1$

Elliptic curves in class 70560ee

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
70560.cl3	70560ee1	\([0, 0, 0, -2315397, -1355792564]\)	\(250094631024064/62015625\)	\(340405734249000000\)	\([2, 2]\)	\(1179648\)	\(2.3517\)	\(\Gamma_0(N)\)-optimal
70560.cl4	70560ee2	\([0, 0, 0, -2039772, -1690732064]\)	\(-2671731885376/1969120125\)	\(-691748023927951872000\)	\([2]\)	\(2359296\)	\(2.6982\)
70560.cl2	70560ee3	\([0, 0, 0, -2593227, -1010005346]\)	\(43919722445768/15380859375\)	\(675408202875000000000\)	\([2]\)	\(2359296\)	\(2.6982\)
70560.cl1	70560ee4	\([0, 0, 0, -37044147, -86781571814]\)	\(128025588102048008/7875\)	\(345808999872000\)	\([2]\)	\(2359296\)	\(2.6982\)

Rank

The elliptic curves in class 70560ee have rank \(1\).

Complex multiplication

The elliptic curves in class 70560ee do not have complex multiplication.

Modular form 70560.2.a.ee

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.