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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 162624.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162624.cc1 | 162624hy1 | \([0, -1, 0, -1008, 11970]\) | \(1000000/63\) | \(7142933952\) | \([2]\) | \(89600\) | \(0.64183\) | \(\Gamma_0(N)\)-optimal |
| 162624.cc2 | 162624hy2 | \([0, -1, 0, 807, 48633]\) | \(8000/147\) | \(-1066678136832\) | \([2]\) | \(179200\) | \(0.98840\) |
Rank
sage: E.rank()
The elliptic curves in class 162624.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 162624.cc do not have complex multiplication.Modular form 162624.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
