Elliptic curve isogeny class with LMFDB label 31824.i (Cremona label 31824o)

• Label: 31824.i
• Number of curves: $4$
• Conductor: $31824$
• CM: no
• Rank: $1$

Elliptic curves in class 31824.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
31824.i1	31824o4	\([0, 0, 0, -3771, -84294]\)	\(7944486372/485537\)	\(362451428352\)	\([2]\)	\(32768\)	\(0.97006\)
31824.i2	31824o2	\([0, 0, 0, -711, 5670]\)	\(212992848/48841\)	\(9114902784\)	\([2, 2]\)	\(16384\)	\(0.62349\)
31824.i3	31824o1	\([0, 0, 0, -666, 6615]\)	\(2800908288/221\)	\(2577744\)	\([2]\)	\(8192\)	\(0.27691\)	\(\Gamma_0(N)\)-optimal
31824.i4	31824o3	\([0, 0, 0, 1629, 35154]\)	\(640412028/1085773\)	\(-810525201408\)	\([2]\)	\(32768\)	\(0.97006\)

Rank

The elliptic curves in class 31824.i have rank \(1\).

Complex multiplication

The elliptic curves in class 31824.i do not have complex multiplication.

Modular form 31824.2.a.i

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.