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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 40560.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40560.cc1 | 40560r2 | \([0, 1, 0, -723376, 165691124]\) | \(4234737878642/1247410125\) | \(12331029336148224000\) | \([2]\) | \(645120\) | \(2.3690\) | |
| 40560.cc2 | 40560r1 | \([0, 1, 0, 121624, 17309124]\) | \(40254822716/49359375\) | \(-243966234096000000\) | \([2]\) | \(322560\) | \(2.0224\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40560.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 40560.cc do not have complex multiplication.Modular form 40560.2.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.
