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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 242550d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.d1 | 242550d1 | \([1, -1, 0, -321792, 70327116]\) | \(74246873427/16940\) | \(840785931562500\) | \([2]\) | \(2359296\) | \(1.8556\) | \(\Gamma_0(N)\)-optimal |
| 242550.d2 | 242550d2 | \([1, -1, 0, -285042, 86974866]\) | \(-51603494067/35870450\) | \(-1780364210083593750\) | \([2]\) | \(4718592\) | \(2.2021\) |
Rank
sage: E.rank()
The elliptic curves in class 242550d have rank \(2\).
Complex multiplication
The elliptic curves in class 242550d do not have complex multiplication.Modular form 242550.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
