Elliptic Curve Isogeny Class with Cremona label 735a (LMFDB label 735.f)

• Label: 735a
• Number of curves: 4
• Conductor: 735
• CM: no
• Rank: 0

Elliptic curves in class 735a

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
735.f3	735a1	[1, 1, 0, -123, -552]	[2]	192	\(\Gamma_0(N)\)-optimal
735.f2	735a2	[1, 1, 0, -368, 1947]	[2, 2]	384
735.f1	735a3	[1, 1, 0, -5513, 155268]	[2]	768
735.f4	735a4	[1, 1, 0, 857, 13462]	[2]	768

Rank

The elliptic curves in class 735a have rank \(0\).

Modular form 735.2.a.f

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.