Show commands:
SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 177744bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177744.v2 | 177744bx1 | \([0, -1, 0, 4481512, -15991753680]\) | \(1349232625/15752961\) | \(-116217805336874360598528\) | \([2]\) | \(12435456\) | \(3.1067\) | \(\Gamma_0(N)\)-optimal |
177744.v1 | 177744bx2 | \([0, -1, 0, -74360648, -230063986512]\) | \(6163717745375/466948881\) | \(3444925316220189380210688\) | \([2]\) | \(24870912\) | \(3.4533\) |
Rank
sage: E.rank()
The elliptic curves in class 177744bx have rank \(1\).
Complex multiplication
The elliptic curves in class 177744bx do not have complex multiplication.Modular form 177744.2.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.