Elliptic curve isogeny class with Cremona label 3648b (LMFDB label 3648.i)

• Label: 3648b
• Number of curves: $4$
• Conductor: $3648$
• CM: no
• Rank: $1$

Elliptic curves in class 3648b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3648.i3	3648b1	\([0, -1, 0, -513, 513]\)	\(57066625/32832\)	\(8606711808\)	\([2]\)	\(2304\)	\(0.59592\)	\(\Gamma_0(N)\)-optimal
3648.i4	3648b2	\([0, -1, 0, 2047, 2049]\)	\(3616805375/2105352\)	\(-551905394688\)	\([2]\)	\(4608\)	\(0.94249\)
3648.i1	3648b3	\([0, -1, 0, -27393, -1735935]\)	\(8671983378625/82308\)	\(21576548352\)	\([2]\)	\(6912\)	\(1.1452\)
3648.i2	3648b4	\([0, -1, 0, -26753, -1821567]\)	\(-8078253774625/846825858\)	\(-221990317719552\)	\([2]\)	\(13824\)	\(1.4918\)

Rank

The elliptic curves in class 3648b have rank \(1\).

Complex multiplication

The elliptic curves in class 3648b do not have complex multiplication.

Modular form 3648.2.a.b

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.