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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 304200g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304200.g1 | 304200g1 | \([0, 0, 0, -126750, 7964125]\) | \(256000/117\) | \(102923255009250000\) | \([2]\) | \(3096576\) | \(1.9593\) | \(\Gamma_0(N)\)-optimal |
304200.g2 | 304200g2 | \([0, 0, 0, 443625, 59868250]\) | \(686000/507\) | \(-7136012347308000000\) | \([2]\) | \(6193152\) | \(2.3059\) |
Rank
sage: E.rank()
The elliptic curves in class 304200g have rank \(1\).
Complex multiplication
The elliptic curves in class 304200g do not have complex multiplication.Modular form 304200.2.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 Cremona 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 Cremona labels.