Elliptic curve isogeny class with Cremona label 324870cn (LMFDB label 324870.cn)

• Label: 324870cn
• Number of curves: $4$
• Conductor: $324870$
• CM: no
• Rank: $0$

Elliptic curves in class 324870cn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
324870.cn4	324870cn1	\([1, 0, 1, -306060053, -7016208163744]\)	\(-26949791983733109138764089/165161952797784563712000\)	\(-19431138584706556136153088000\)	\([2]\)	\(311427072\)	\(4.1117\)	\(\Gamma_0(N)\)-optimal
324870.cn3	324870cn2	\([1, 0, 1, -7685005333, -258782869539232]\)	\(426646307804307769001905914169/998470877001641316000000\)	\(117469100208366099186084000000\)	\([2, 2]\)	\(622854144\)	\(4.4583\)
324870.cn2	324870cn3	\([1, 0, 1, -10542195333, -48935978551232]\)	\(1101358349464662961278219354169/628567168199833707765102000\)	\(73950298771542235884856485198000\)	\([4]\)	\(1245708288\)	\(4.8049\)
324870.cn1	324870cn4	\([1, 0, 1, -122890939813, -16581666572777344]\)	\(1744596788171434949302427839201849/9588363813082031250000\)	\(1128061414245287894531250000\)	\([2]\)	\(1245708288\)	\(4.8049\)

Rank

The elliptic curves in class 324870cn have rank \(0\).

Complex multiplication

The elliptic curves in class 324870cn do not have complex multiplication.

Modular form 324870.2.a.cn

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.