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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 14400.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14400.bg1 | 14400ev4 | \([0, 0, 0, -11923500, 15795650000]\) | \(502270291349/1889568\) | \(705277476864000000000\) | \([2]\) | \(614400\) | \(2.8598\) | |
| 14400.bg2 | 14400ev2 | \([0, 0, 0, -763500, -256750000]\) | \(131872229/18\) | \(6718464000000000\) | \([2]\) | \(122880\) | \(2.0550\) | |
| 14400.bg3 | 14400ev3 | \([0, 0, 0, -403500, 474050000]\) | \(-19465109/248832\) | \(-92876046336000000000\) | \([2]\) | \(307200\) | \(2.5132\) | |
| 14400.bg4 | 14400ev1 | \([0, 0, 0, -43500, -4750000]\) | \(-24389/12\) | \(-4478976000000000\) | \([2]\) | \(61440\) | \(1.7085\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14400.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 14400.bg do not have complex multiplication.Modular form 14400.2.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.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
