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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 26640bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26640.j3 | 26640bg1 | \([0, 0, 0, -10803, -236302]\) | \(46694890801/18944000\) | \(56566480896000\) | \([2]\) | \(55296\) | \(1.3367\) | \(\Gamma_0(N)\)-optimal |
| 26640.j4 | 26640bg2 | \([0, 0, 0, 35277, -1720078]\) | \(1625964918479/1369000000\) | \(-4087812096000000\) | \([2]\) | \(110592\) | \(1.6832\) | |
| 26640.j1 | 26640bg3 | \([0, 0, 0, -759603, -254816782]\) | \(16232905099479601/4052240\) | \(12099923804160\) | \([2]\) | \(165888\) | \(1.8860\) | |
| 26640.j2 | 26640bg4 | \([0, 0, 0, -756723, -256844878]\) | \(-16048965315233521/256572640900\) | \(-766121800565145600\) | \([2]\) | \(331776\) | \(2.2325\) |
Rank
sage: E.rank()
The elliptic curves in class 26640bg have rank \(0\).
Complex multiplication
The elliptic curves in class 26640bg do not have complex multiplication.Modular form 26640.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
