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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 98736.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.cc1 | 98736cs2 | \([0, -1, 0, -114869, -14954883]\) | \(-23100424192/14739\) | \(-106950809923584\) | \([]\) | \(583200\) | \(1.6329\) | |
| 98736.cc2 | 98736cs1 | \([0, -1, 0, 1291, -86403]\) | \(32768/459\) | \(-3330648059904\) | \([]\) | \(194400\) | \(1.0836\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 98736.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 98736.cc do not have complex multiplication.Modular form 98736.2.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 LMFDB 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 LMFDB labels.
