Elliptic curve isogeny class with Cremona label 31680cj (LMFDB label 31680.y)

• Label: 31680cj
• Number of curves: $2$
• Conductor: $31680$
• CM: no
• Rank: $1$

Elliptic curves in class 31680cj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
31680.y2	31680cj1	\([0, 0, 0, -48, 2072]\)	\(-16384/2475\)	\(-1847577600\)	\([2]\)	\(12288\)	\(0.45748\)	\(\Gamma_0(N)\)-optimal
31680.y1	31680cj2	\([0, 0, 0, -2748, 54992]\)	\(192143824/1815\)	\(21678243840\)	\([2]\)	\(24576\)	\(0.80405\)

Rank

The elliptic curves in class 31680cj have rank \(1\).

Complex multiplication

The elliptic curves in class 31680cj do not have complex multiplication.

Modular form 31680.2.a.cj

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.