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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 56448.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56448.ch1 | 56448cs1 | \([0, 0, 0, -1470, 17836]\) | \(16000/3\) | \(65868380928\) | \([2]\) | \(46080\) | \(0.79382\) | \(\Gamma_0(N)\)-optimal |
| 56448.ch2 | 56448cs2 | \([0, 0, 0, 2940, 104272]\) | \(4000/9\) | \(-6323364569088\) | \([2]\) | \(92160\) | \(1.1404\) |
Rank
sage: E.rank()
The elliptic curves in class 56448.ch have rank \(0\).
Complex multiplication
The elliptic curves in class 56448.ch do not have complex multiplication.Modular form 56448.2.a.ch
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.
