Show commands:
SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 20286bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20286.cc2 | 20286bx1 | \([1, -1, 1, -230, 1077045]\) | \(-15625/5842368\) | \(-501077240814528\) | \([2]\) | \(73728\) | \(1.4995\) | \(\Gamma_0(N)\)-optimal |
20286.cc1 | 20286bx2 | \([1, -1, 1, -158990, 24065493]\) | \(5182207647625/91449288\) | \(7843250699971848\) | \([2]\) | \(147456\) | \(1.8461\) |
Rank
sage: E.rank()
The elliptic curves in class 20286bx have rank \(0\).
Complex multiplication
The elliptic curves in class 20286bx do not have complex multiplication.Modular form 20286.2.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 Cremona 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 Cremona labels.