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SageMath
E = EllipticCurve("ga1")
E.isogeny_class()
Elliptic curves in class 270400ga
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270400.ga2 | 270400ga1 | \([0, 0, 0, -591500, -109850000]\) | \(37044/13\) | \(8031810176000000000\) | \([2]\) | \(4300800\) | \(2.3288\) | \(\Gamma_0(N)\)-optimal |
| 270400.ga1 | 270400ga2 | \([0, 0, 0, -3971500, 2965950000]\) | \(5606442/169\) | \(208827064576000000000\) | \([2]\) | \(8601600\) | \(2.6754\) |
Rank
sage: E.rank()
The elliptic curves in class 270400ga have rank \(0\).
Complex multiplication
The elliptic curves in class 270400ga do not have complex multiplication.Modular form 270400.2.a.ga
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.
