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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 15600.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.bt1 | 15600cr2 | \([0, 1, 0, -1409208, -642314412]\) | \(38686490446661/141927552\) | \(1135420416000000000\) | \([2]\) | \(430080\) | \(2.3249\) | |
| 15600.bt2 | 15600cr1 | \([0, 1, 0, -129208, 245588]\) | \(29819839301/17252352\) | \(138018816000000000\) | \([2]\) | \(215040\) | \(1.9783\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15600.bt have rank \(0\).
Complex multiplication
The elliptic curves in class 15600.bt do not have complex multiplication.Modular form 15600.2.a.bt
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.
