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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 25536.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25536.ce1 | 25536bj4 | \([0, 1, 0, -12929, -473889]\) | \(1823652903746/328593657\) | \(43069427810304\) | \([2]\) | \(81920\) | \(1.3352\) | |
| 25536.ce2 | 25536bj2 | \([0, 1, 0, -3809, 82431]\) | \(93280467172/7800849\) | \(511236440064\) | \([2, 2]\) | \(40960\) | \(0.98860\) | |
| 25536.ce3 | 25536bj1 | \([0, 1, 0, -3729, 86415]\) | \(350104249168/2793\) | \(45760512\) | \([2]\) | \(20480\) | \(0.64202\) | \(\Gamma_0(N)\)-optimal |
| 25536.ce4 | 25536bj3 | \([0, 1, 0, 4031, 385055]\) | \(55251546334/517244049\) | \(-67796211990528\) | \([4]\) | \(81920\) | \(1.3352\) |
Rank
sage: E.rank()
The elliptic curves in class 25536.ce have rank \(1\).
Complex multiplication
The elliptic curves in class 25536.ce do not have complex multiplication.Modular form 25536.2.a.ce
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
