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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 138600.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
138600.cb1 | 138600ec2 | \([0, 0, 0, -5128275, -3135181250]\) | \(1278763167594532/375974556419\) | \(4385367226071216000000\) | \([2]\) | \(5898240\) | \(2.8586\) | |
138600.cb2 | 138600ec1 | \([0, 0, 0, 861225, -326105750]\) | \(24226243449392/29774625727\) | \(-86822808619932000000\) | \([2]\) | \(2949120\) | \(2.5120\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 138600.cb have rank \(1\).
Complex multiplication
The elliptic curves in class 138600.cb do not have complex multiplication.Modular form 138600.2.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.