Elliptic curve isogeny class with Cremona label 270480cv (LMFDB label 270480.cv)

• Label: 270480cv
• Number of curves: $4$
• Conductor: $270480$
• CM: no
• Rank: $2$

Elliptic curves in class 270480cv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
270480.cv3	270480cv1	\([0, -1, 0, -5700, -163680]\)	\(680136784/345\)	\(10390759680\)	\([2]\)	\(294912\)	\(0.87404\)	\(\Gamma_0(N)\)-optimal
270480.cv2	270480cv2	\([0, -1, 0, -6680, -102528]\)	\(273671716/119025\)	\(14339248358400\)	\([2, 2]\)	\(589824\)	\(1.2206\)
270480.cv1	270480cv3	\([0, -1, 0, -51760, 4477600]\)	\(63649751618/1164375\)	\(280550511360000\)	\([2]\)	\(1179648\)	\(1.5672\)
270480.cv4	270480cv4	\([0, -1, 0, 22720, -784608]\)	\(5382838942/4197615\)	\(-1011394984212480\)	\([2]\)	\(1179648\)	\(1.5672\)

Rank

The elliptic curves in class 270480cv have rank \(2\).

Complex multiplication

The elliptic curves in class 270480cv do not have complex multiplication.

Modular form 270480.2.a.cv

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.