Elliptic curve isogeny class with Cremona label 52416br (LMFDB label 52416.be)

• Label: 52416br
• Number of curves: $4$
• Conductor: $52416$
• CM: no
• Rank: $2$

Elliptic curves in class 52416br

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
52416.be4	52416br1	\([0, 0, 0, 9, 1836]\)	\(1728/31213\)	\(-1456273728\)	\([2]\)	\(18432\)	\(0.43716\)	\(\Gamma_0(N)\)-optimal
52416.be3	52416br2	\([0, 0, 0, -2196, 38880]\)	\(392223168/8281\)	\(24726933504\)	\([2, 2]\)	\(36864\)	\(0.78374\)
52416.be2	52416br3	\([0, 0, 0, -4716, -66960]\)	\(485587656/199927\)	\(4775830585344\)	\([2]\)	\(73728\)	\(1.1303\)
52416.be1	52416br4	\([0, 0, 0, -34956, 2515536]\)	\(197747699976/91\)	\(2173796352\)	\([2]\)	\(73728\)	\(1.1303\)

Rank

The elliptic curves in class 52416br have rank \(2\).

Complex multiplication

The elliptic curves in class 52416br do not have complex multiplication.

Modular form 52416.2.a.br

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.