Show commands:
SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 85176.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
85176.bx1 | 85176bn2 | \([0, 0, 0, -18759, 988650]\) | \(21882096/7\) | \(233540326656\) | \([2]\) | \(147456\) | \(1.1562\) | |
85176.bx2 | 85176bn1 | \([0, 0, 0, -1014, 19773]\) | \(-55296/49\) | \(-102173892912\) | \([2]\) | \(73728\) | \(0.80960\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 85176.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 85176.bx do not have complex multiplication.Modular form 85176.2.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.