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Properties

Label 177450di
Number of curves $2$
Conductor $177450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("di1")
 
E.isogeny_class()
 

Elliptic curves in class 177450di

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.gp2 177450di1 \([1, 1, 1, 3016562, -22783692469]\) \(40251338884511/2997011332224\) \(-226031269866887394000000\) \([]\) \(27659520\) \(3.1608\) \(\Gamma_0(N)\)-optimal
177450.gp1 177450di2 \([1, 1, 1, -15524745688, -744541018152469]\) \(-5486773802537974663600129/2635437714\) \(-198761788701166031250\) \([]\) \(193616640\) \(4.1337\)  

Rank

sage: E.rank()
 

The elliptic curves in class 177450di have rank \(1\).

Complex multiplication

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

Modular form 177450.2.a.di

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} + q^{9} - 5 q^{11} - q^{12} + q^{14} + q^{16} + 3 q^{17} + q^{18} + q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.