Properties

Label 53361.bi
Number of curves $3$
Conductor $53361$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 53361.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53361.bi1 53361ba1 \([0, 0, 1, -4766916, -4005962942]\) \(-78843215872/539\) \(-81895614230750859\) \([]\) \(1152000\) \(2.4262\) \(\Gamma_0(N)\)-optimal
53361.bi2 53361ba2 \([0, 0, 1, -2632476, -7601160317]\) \(-13278380032/156590819\) \(-23792395741931970307539\) \([]\) \(3456000\) \(2.9755\)  
53361.bi3 53361ba3 \([0, 0, 1, 23514414, 196749858478]\) \(9463555063808/115539436859\) \(-17555052225311429925028779\) \([]\) \(10368000\) \(3.5248\)  

Rank

sage: E.rank()
 

The elliptic curves in class 53361.bi have rank \(0\).

Complex multiplication

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

Modular form 53361.2.a.bi

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} + 3 q^{5} - 4 q^{13} + 4 q^{16} + 6 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.