Elliptic curve isogeny class with LMFDB label 31680.cc (Cremona label 31680bo)

• Label: 31680.cc
• Number of curves: $4$
• Conductor: $31680$
• CM: no
• Rank: $1$

Elliptic curves in class 31680.cc

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
31680.cc1	31680bo4	[0, 0, 0, -255612, 49741616]	[2]	165888
31680.cc2	31680bo3	[0, 0, 0, -16032, 771464]	[2]	82944
31680.cc3	31680bo2	[0, 0, 0, -3612, 47216]	[2]	55296
31680.cc4	31680bo1	[0, 0, 0, -1632, -24856]	[2]	27648	\(\Gamma_0(N)\)-optimal

Rank

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

Complex multiplication

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

Modular form 31680.2.a.cc

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.