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SageMath
E = EllipticCurve("rp1")
E.isogeny_class()
Elliptic curves in class 705600.rp
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.rp1 | \([0, 0, 0, -120319500, 505256150000]\) | \(4386781853/27216\) | \(1195115903557632000000000\) | \([2]\) | \(117964800\) | \(3.4580\) |
705600.rp2 | \([0, 0, 0, -49759500, 1093020950000]\) | \(-310288733/11573604\) | \(-508223037987883008000000000\) | \([2]\) | \(235929600\) | \(3.8046\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.rp have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.rp do not have complex multiplication.Modular form 705600.2.a.rp
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.