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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 83300.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83300.bg1 | 83300j2 | \([0, 1, 0, -9228, 350468]\) | \(-115431760/4913\) | \(-3699261036800\) | \([]\) | \(81648\) | \(1.1778\) | |
| 83300.bg2 | 83300j1 | \([0, 1, 0, 572, 1588]\) | \(27440/17\) | \(-12800211200\) | \([]\) | \(27216\) | \(0.62851\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 83300.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 83300.bg do not have complex multiplication.Modular form 83300.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
