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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 372645cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
372645.cc2 | 372645cc1 | \([1, -1, 1, -93827, 10650826]\) | \(2803221/125\) | \(4073385746327625\) | \([2]\) | \(2211840\) | \(1.7579\) | \(\Gamma_0(N)\)-optimal |
372645.cc1 | 372645cc2 | \([1, -1, 1, -253532, -35088686]\) | \(55306341/15625\) | \(509173218290953125\) | \([2]\) | \(4423680\) | \(2.1045\) |
Rank
sage: E.rank()
The elliptic curves in class 372645cc have rank \(1\).
Complex multiplication
The elliptic curves in class 372645cc do not have complex multiplication.Modular form 372645.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.