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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 57330.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57330.e1 | 57330h2 | \([1, -1, 0, -3880515, -1471909419]\) | \(2034416504287874043/882294347833600\) | \(2802628288663430572800\) | \([2]\) | \(3686400\) | \(2.8116\) | |
| 57330.e2 | 57330h1 | \([1, -1, 0, 823485, -170783019]\) | \(19441890357117957/15208161280000\) | \(-48309074093629440000\) | \([2]\) | \(1843200\) | \(2.4650\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57330.e have rank \(1\).
Complex multiplication
The elliptic curves in class 57330.e do not have complex multiplication.Modular form 57330.2.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.
