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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 327990.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 327990.d1 | 327990d4 | \([1, 1, 0, -1005853, -368944997]\) | \(189208196468929/10860320250\) | \(6459971758228550250\) | \([2]\) | \(7257600\) | \(2.3635\) | |
| 327990.d2 | 327990d2 | \([1, 1, 0, -173263, 27564637]\) | \(967068262369/4928040\) | \(2931313118820840\) | \([2]\) | \(2419200\) | \(1.8142\) | |
| 327990.d3 | 327990d1 | \([1, 1, 0, -5063, 888117]\) | \(-24137569/561600\) | \(-334052777073600\) | \([2]\) | \(1209600\) | \(1.4676\) | \(\Gamma_0(N)\)-optimal |
| 327990.d4 | 327990d3 | \([1, 1, 0, 45397, -23504247]\) | \(17394111071/411937500\) | \(-245030031794437500\) | \([2]\) | \(3628800\) | \(2.0169\) |
Rank
sage: E.rank()
The elliptic curves in class 327990.d have rank \(0\).
Complex multiplication
The elliptic curves in class 327990.d do not have complex multiplication.Modular form 327990.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
