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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 369600.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.e1 | 369600e1 | \([0, -1, 0, -46208, -1487838]\) | \(87292033856/42706587\) | \(5338323375000000\) | \([2]\) | \(2211840\) | \(1.7111\) | \(\Gamma_0(N)\)-optimal |
| 369600.e2 | 369600e2 | \([0, -1, 0, 168167, -11563463]\) | \(65743598656/45196767\) | \(-361574136000000000\) | \([2]\) | \(4423680\) | \(2.0577\) |
Rank
sage: E.rank()
The elliptic curves in class 369600.e have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.e do not have complex multiplication.Modular form 369600.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
