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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 314600.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 314600.bg1 | 314600bg2 | \([0, 0, 0, -28435, -1796850]\) | \(5606442/169\) | \(76644815104000\) | \([2]\) | \(896000\) | \(1.4406\) | |
| 314600.bg2 | 314600bg1 | \([0, 0, 0, -4235, 66550]\) | \(37044/13\) | \(2947877504000\) | \([2]\) | \(448000\) | \(1.0940\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 314600.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 314600.bg do not have complex multiplication.Modular form 314600.2.a.bg
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.
