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Properties

Label 177450.hz
Number of curves $2$
Conductor $177450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("hz1")
 
E.isogeny_class()
 

Elliptic curves in class 177450.hz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.hz1 177450l2 \([1, 0, 0, -59238, -5876508]\) \(-7620530425/526848\) \(-1589371667520000\) \([]\) \(1516320\) \(1.6678\)  
177450.hz2 177450l1 \([1, 0, 0, 4137, -7983]\) \(2595575/1512\) \(-4561334505000\) \([]\) \(505440\) \(1.1185\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 177450.hz have rank \(0\).

Complex multiplication

The elliptic curves in class 177450.hz do not have complex multiplication.

Modular form 177450.2.a.hz

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} - 6 q^{11} + q^{12} - q^{14} + q^{16} + 3 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.