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SageMath
E = EllipticCurve("yc1")
E.isogeny_class()
Elliptic curves in class 705600.yc
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.yc1 | \([0, 0, 0, -2263800, 991613000]\) | \(2725888/675\) | \(317712018632400000000\) | \([2]\) | \(16515072\) | \(2.6443\) |
705600.yc2 | \([0, 0, 0, 5453700, 6285818000]\) | \(2382032/3645\) | \(-27450318409839360000000\) | \([2]\) | \(33030144\) | \(2.9909\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.yc have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.yc do not have complex multiplication.Modular form 705600.2.a.yc
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.