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 \(0\).

Complex multiplication

The elliptic curves in class 735a do not have complex multiplication.

Modular form 735.2.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.