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SageMath
E = EllipticCurve("cbm1")
E.isogeny_class()
Elliptic curves in class 705600.cbm
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.cbm1 | \([0, 0, 0, -43938300, 112169918000]\) | \(-177953104/125\) | \(-6589582608672000000000\) | \([]\) | \(69672960\) | \(3.1229\) |
705600.cbm2 | \([0, 0, 0, 42497700, 476411222000]\) | \(161017136/1953125\) | \(-102962228260500000000000000\) | \([]\) | \(209018880\) | \(3.6722\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.cbm have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.cbm do not have complex multiplication.Modular form 705600.2.a.cbm
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.