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SageMath
E = EllipticCurve("ez1")
E.isogeny_class()
Elliptic curves in class 44352.ez
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44352.ez1 | 44352c2 | \([0, 0, 0, -23868, -1216080]\) | \(4662947952/717409\) | \(231354553909248\) | \([2]\) | \(184320\) | \(1.4798\) | |
| 44352.ez2 | 44352c1 | \([0, 0, 0, 2592, -104760]\) | \(95551488/290521\) | \(-5855564639232\) | \([2]\) | \(92160\) | \(1.1332\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44352.ez have rank \(1\).
Complex multiplication
The elliptic curves in class 44352.ez do not have complex multiplication.Modular form 44352.2.a.ez
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.
