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Properties

Label 176610dm
Number of curves $2$
Conductor $176610$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dm1")
 
E.isogeny_class()
 

Elliptic curves in class 176610dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176610.d1 176610dm1 \([1, 1, 0, -1506248, 710903208]\) \(-635368419908209/1096200\) \(-652045324480200\) \([]\) \(3386880\) \(2.1029\) \(\Gamma_0(N)\)-optimal
176610.d2 176610dm2 \([1, 1, 0, -1077338, 1124316942]\) \(-232483583073169/784258781250\) \(-466495412786537531250\) \([]\) \(10160640\) \(2.6522\)  

Rank

sage: E.rank()
 

The elliptic curves in class 176610dm have rank \(0\).

Complex multiplication

The elliptic curves in class 176610dm do not have complex multiplication.

Modular form 176610.2.a.dm

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - 3 q^{11} - q^{12} + 5 q^{13} - q^{14} + q^{15} + q^{16} - q^{18} - 5 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.