Properties

Label 57222.bv
Number of curves $2$
Conductor $57222$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bv1")
 
E.isogeny_class()
 

Elliptic curves in class 57222.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57222.bv1 57222br2 \([1, -1, 1, -123643371614, 16734208408465133]\) \(2418067440128989194388361/8359273562112\) \(722663897074725458457133056\) \([2]\) \(222265344\) \(4.7975\)  
57222.bv2 57222br1 \([1, -1, 1, -7731159134, 261228419657453]\) \(591139158854005457801/1097587482427392\) \(94887054663038733073772445696\) \([2]\) \(111132672\) \(4.4510\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 57222.bv have rank \(0\).

Complex multiplication

The elliptic curves in class 57222.bv do not have complex multiplication.

Modular form 57222.2.a.bv

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 2 q^{5} + 4 q^{7} + q^{8} + 2 q^{10} + q^{11} + 4 q^{14} + q^{16} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.