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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 273600eh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 273600.eh1 | 273600eh1 | \([0, 0, 0, -829200, -271051000]\) | \(5405726654464/407253125\) | \(4750200450000000000\) | \([2]\) | \(4423680\) | \(2.3290\) | \(\Gamma_0(N)\)-optimal |
| 273600.eh2 | 273600eh2 | \([0, 0, 0, 795300, -1203514000]\) | \(298091207216/3525390625\) | \(-657922500000000000000\) | \([2]\) | \(8847360\) | \(2.6755\) |
Rank
sage: E.rank()
The elliptic curves in class 273600eh have rank \(1\).
Complex multiplication
The elliptic curves in class 273600eh do not have complex multiplication.Modular form 273600.2.a.eh
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.
