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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 22800.dl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22800.dl1 | 22800cx2 | \([0, 1, 0, -9330408, 10966699188]\) | \(1403607530712116449/39475350\) | \(2526422400000000\) | \([2]\) | \(645120\) | \(2.4659\) | |
22800.dl2 | 22800cx1 | \([0, 1, 0, -582408, 171667188]\) | \(-341370886042369/1817528220\) | \(-116321806080000000\) | \([2]\) | \(322560\) | \(2.1194\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22800.dl have rank \(1\).
Complex multiplication
The elliptic curves in class 22800.dl do not have complex multiplication.Modular form 22800.2.a.dl
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.