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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 336336cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
336336.cc2 | 336336cc1 | \([0, -1, 0, 1552, 29184]\) | \(857375/1287\) | \(-620192821248\) | \([2]\) | \(393216\) | \(0.94816\) | \(\Gamma_0(N)\)-optimal |
336336.cc1 | 336336cc2 | \([0, -1, 0, -10208, 302016]\) | \(244140625/61347\) | \(29562524479488\) | \([2]\) | \(786432\) | \(1.2947\) |
Rank
sage: E.rank()
The elliptic curves in class 336336cc have rank \(1\).
Complex multiplication
The elliptic curves in class 336336cc do not have complex multiplication.Modular form 336336.2.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.