Elliptic curve isogeny class with LMFDB label 53361.r (Cremona label 53361bm)

• Label: 53361.r
• Number of curves: $2$
• Conductor: $53361$
• CM: no
• Rank: $2$

Elliptic curves in class 53361.r

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
53361.r1	53361bm2	[1, -1, 1, -1601942, 780829382]	[]	570240
53361.r2	53361bm1	[1, -1, 1, -1112, -55492]	[]	51840	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 53361.r have rank \(2\).

Complex multiplication

The elliptic curves in class 53361.r do not have complex multiplication.

Modular form 53361.2.a.r

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.