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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 38720.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38720.cc1 | 38720l2 | \([0, 1, 0, -45999521, 120066720959]\) | \(-23178622194826561/1610510\) | \(-747927425806499840\) | \([]\) | \(2304000\) | \(2.8837\) | |
38720.cc2 | 38720l1 | \([0, 1, 0, 77279, 33404479]\) | \(109902239/1100000\) | \(-510844495462400000\) | \([]\) | \(460800\) | \(2.0790\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38720.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 38720.cc do not have complex multiplication.Modular form 38720.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.