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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 381938cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381938.cc2 | 381938cc1 | \([1, 1, 1, 91506, 184427759]\) | \(23/4\) | \(-14736837178090710244\) | \([]\) | \(13115520\) | \(2.3573\) | \(\Gamma_0(N)\)-optimal |
381938.cc1 | 381938cc2 | \([1, 1, 1, -21869929, 39363627799]\) | \(-313994137/64\) | \(-235789394849451363904\) | \([]\) | \(39346560\) | \(2.9066\) |
Rank
sage: E.rank()
The elliptic curves in class 381938cc have rank \(0\).
Complex multiplication
The elliptic curves in class 381938cc do not have complex multiplication.Modular form 381938.2.a.cc
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 Cremona 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 Cremona labels.