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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 98736.dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.dc1 | 98736da2 | \([0, 1, 0, -2145295192, 27261769244180]\) | \(150476552140919246594353/42832838728685592576\) | \(310808521158774690076799533056\) | \([2]\) | \(93450240\) | \(4.3658\) | |
| 98736.dc2 | 98736da1 | \([0, 1, 0, -797219672, -8327963714028]\) | \(7722211175253055152433/340131399900069888\) | \(2468100189955554143662768128\) | \([2]\) | \(46725120\) | \(4.0192\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 98736.dc have rank \(0\).
Complex multiplication
The elliptic curves in class 98736.dc do not have complex multiplication.Modular form 98736.2.a.dc
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.
