Elliptic Curve Isogeny Class with LMFDB label 12705.g (Cremona label 12705n)

• Label: 12705.g
• Number of curves: 4
• Conductor: 12705
• CM: no
• Rank: 0

Elliptic curves in class 12705.g

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
12705.g1	12705n3	[1, 0, 0, -13615, 610292]	[2]	23040
12705.g2	12705n2	[1, 0, 0, -910, 8075]	[2, 2]	11520
12705.g3	12705n1	[1, 0, 0, -305, -1968]	[2]	5760	\(\Gamma_0(N)\)-optimal
12705.g4	12705n4	[1, 0, 0, 2115, 51030]	[2]	23040

Rank

The elliptic curves in class 12705.g have rank \(0\).

Modular form 12705.2.a.g

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.