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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 9702.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9702.cb1 | 9702bj2 | \([1, -1, 1, -101152694, 391599688645]\) | \(144106117295241933/247808\) | \(196828949783144448\) | \([2]\) | \(827904\) | \(3.0073\) | |
9702.cb2 | 9702bj1 | \([1, -1, 1, -6320054, 6123973573]\) | \(-35148950502093/46137344\) | \(-36645971741443620864\) | \([2]\) | \(413952\) | \(2.6608\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9702.cb have rank \(0\).
Complex multiplication
The elliptic curves in class 9702.cb do not have complex multiplication.Modular form 9702.2.a.cb
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.