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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 57330.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57330.h1 | 57330bt2 | \([1, -1, 0, -20295, -991845]\) | \(10779215329/1232010\) | \(105664718733210\) | \([2]\) | \(276480\) | \(1.4232\) | |
57330.h2 | 57330bt1 | \([1, -1, 0, 1755, -78975]\) | \(6967871/35100\) | \(-3010390847100\) | \([2]\) | \(138240\) | \(1.0766\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57330.h have rank \(0\).
Complex multiplication
The elliptic curves in class 57330.h do not have complex multiplication.Modular form 57330.2.a.h
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.