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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 58800.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.bg1 | 58800hd1 | \([0, -1, 0, -3430408, -2444351888]\) | \(-14822892630025/42\) | \(-12649620480000\) | \([]\) | \(691200\) | \(2.1707\) | \(\Gamma_0(N)\)-optimal |
| 58800.bg2 | 58800hd2 | \([0, -1, 0, 430792, -7545683088]\) | \(46969655/130691232\) | \(-24601108405708800000000\) | \([]\) | \(3456000\) | \(2.9754\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 58800.bg do not have complex multiplication.Modular form 58800.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
