Show commands:
SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 54150.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54150.bx1 | 54150bl2 | \([1, 1, 1, -16813, -508969]\) | \(4904335099/1822500\) | \(195320742187500\) | \([2]\) | \(184320\) | \(1.4421\) | |
54150.bx2 | 54150bl1 | \([1, 1, 1, -7313, 232031]\) | \(403583419/10800\) | \(1157456250000\) | \([2]\) | \(92160\) | \(1.0955\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54150.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 54150.bx do not have complex multiplication.Modular form 54150.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.