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Properties

Label 56350.bz
Number of curves $2$
Conductor $56350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 56350.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56350.bz1 56350bp2 \([1, 1, 1, -741763, -230514719]\) \(24553362849625/1755162752\) \(3226455353282000000\) \([2]\) \(1548288\) \(2.2984\)  
56350.bz2 56350bp1 \([1, 1, 1, 42237, -15698719]\) \(4533086375/60669952\) \(-111527487232000000\) \([2]\) \(774144\) \(1.9519\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 56350.bz have rank \(0\).

Complex multiplication

The elliptic curves in class 56350.bz do not have complex multiplication.

Modular form 56350.2.a.bz

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{8} + q^{9} + 4 q^{11} + 2 q^{12} + q^{16} + 6 q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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.