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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 346560.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
346560.g1 | 346560g2 | \([0, -1, 0, -2917361, -1291734639]\) | \(519388144/164025\) | \(867186272308436582400\) | \([2]\) | \(14008320\) | \(2.7217\) | |
346560.g2 | 346560g1 | \([0, -1, 0, 512139, -137364939]\) | \(44957696/50625\) | \(-16728130252863360000\) | \([2]\) | \(7004160\) | \(2.3751\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346560.g have rank \(1\).
Complex multiplication
The elliptic curves in class 346560.g do not have complex multiplication.Modular form 346560.2.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.