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SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 270400.gb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270400.gb1 | 270400gb2 | \([0, 0, 0, -158860, -23727600]\) | \(5606442/169\) | \(13364932132864000\) | \([2]\) | \(1720320\) | \(1.8707\) | |
| 270400.gb2 | 270400gb1 | \([0, 0, 0, -23660, 878800]\) | \(37044/13\) | \(514035851264000\) | \([2]\) | \(860160\) | \(1.5241\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270400.gb have rank \(1\).
Complex multiplication
The elliptic curves in class 270400.gb do not have complex multiplication.Modular form 270400.2.a.gb
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.
