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SageMath
E = EllipticCurve("gm1")
E.isogeny_class()
Elliptic curves in class 283920gm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 283920.gm3 | 283920gm1 | \([0, 1, 0, -9520, 222548]\) | \(4826809/1680\) | \(33214624235520\) | \([2]\) | \(884736\) | \(1.2961\) | \(\Gamma_0(N)\)-optimal |
| 283920.gm2 | 283920gm2 | \([0, 1, 0, -63600, -6029100]\) | \(1439069689/44100\) | \(871883886182400\) | \([2, 2]\) | \(1769472\) | \(1.6426\) | |
| 283920.gm4 | 283920gm3 | \([0, 1, 0, 17520, -20273772]\) | \(30080231/9003750\) | \(-178009626762240000\) | \([2]\) | \(3538944\) | \(1.9892\) | |
| 283920.gm1 | 283920gm4 | \([0, 1, 0, -1010000, -391024620]\) | \(5763259856089/5670\) | \(112099356794880\) | \([2]\) | \(3538944\) | \(1.9892\) |
Rank
sage: E.rank()
The elliptic curves in class 283920gm have rank \(0\).
Complex multiplication
The elliptic curves in class 283920gm do not have complex multiplication.Modular form 283920.2.a.gm
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
