Show commands:
SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 57150.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57150.bx1 | 57150ba2 | \([1, -1, 1, -29135, -1906793]\) | \(5558063491395/65024\) | \(31996684800\) | \([]\) | \(139968\) | \(1.1663\) | |
57150.bx2 | 57150ba1 | \([1, -1, 1, -560, 747]\) | \(28724783355/16387064\) | \(11061268200\) | \([]\) | \(46656\) | \(0.61702\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57150.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 57150.bx do not have complex multiplication.Modular form 57150.2.a.bx
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.