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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 57330.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57330.g1 | 57330bq2 | \([1, -1, 0, -880245, -316868679]\) | \(2564040033703/7312500\) | \(215117512615687500\) | \([2]\) | \(1032192\) | \(2.1973\) | |
57330.g2 | 57330bq1 | \([1, -1, 0, -77625, -475875]\) | \(1758416743/1014000\) | \(29829628416042000\) | \([2]\) | \(516096\) | \(1.8507\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57330.g have rank \(0\).
Complex multiplication
The elliptic curves in class 57330.g do not have complex multiplication.Modular form 57330.2.a.g
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.