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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 177450.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177450.v1 | 177450ik2 | \([1, 1, 0, -7414540, 7712580400]\) | \(74714744246072741/613043357472\) | \(369880399404508356000\) | \([2]\) | \(10321920\) | \(2.7731\) | |
177450.v2 | 177450ik1 | \([1, 1, 0, -789740, -71559600]\) | \(90283180649381/48614372352\) | \(29331536249748096000\) | \([2]\) | \(5160960\) | \(2.4265\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 177450.v have rank \(0\).
Complex multiplication
The elliptic curves in class 177450.v do not have complex multiplication.Modular form 177450.2.a.v
sage: E.q_eigenform(10)
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.