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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 44352ee
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44352.d2 | 44352ee1 | \([0, 0, 0, -233292, 67736720]\) | \(-7347774183121/6119866368\) | \(-1169524675647111168\) | \([2]\) | \(1032192\) | \(2.1648\) | \(\Gamma_0(N)\)-optimal |
| 44352.d1 | 44352ee2 | \([0, 0, 0, -4288332, 3417199760]\) | \(45637459887836881/13417633152\) | \(2564149626223460352\) | \([2]\) | \(2064384\) | \(2.5114\) |
Rank
sage: E.rank()
The elliptic curves in class 44352ee have rank \(0\).
Complex multiplication
The elliptic curves in class 44352ee do not have complex multiplication.Modular form 44352.2.a.ee
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.
