Show commands:
SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 24150.bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24150.bt1 | 24150br2 | \([1, 1, 1, -9013, 320531]\) | \(5182207647625/91449288\) | \(1428895125000\) | \([2]\) | \(55296\) | \(1.1286\) | |
24150.bt2 | 24150br1 | \([1, 1, 1, -13, 14531]\) | \(-15625/5842368\) | \(-91287000000\) | \([2]\) | \(27648\) | \(0.78199\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24150.bt have rank \(1\).
Complex multiplication
The elliptic curves in class 24150.bt do not have complex multiplication.Modular form 24150.2.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.