Elliptic Curve Isogeny Class with Cremona label 105a (LMFDB label 105.a)

• Label: 105a
• Number of curves: 4
• Conductor: 105
• CM: no
• Rank: 0

Elliptic curves in class 105a

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
105.a3	105a1	[1, 0, 1, -3, 1]	[2]	4	\(\Gamma_0(N)\)-optimal
105.a2	105a2	[1, 0, 1, -8, -7]	[2, 2]	8
105.a1	105a3	[1, 0, 1, -113, -469]	[2]	16
105.a4	105a4	[1, 0, 1, 17, -37]	[4]	16

Rank

The elliptic curves in class 105a have rank \(0\).

Modular form 105.2.a.a

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.