Show commands:
SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 185150bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185150.j2 | 185150bu1 | \([1, 1, 0, -45, -35]\) | \(788785/448\) | \(5924800\) | \([]\) | \(34560\) | \(-0.010554\) | \(\Gamma_0(N)\)-optimal |
185150.j1 | 185150bu2 | \([1, 1, 0, -2345, 42745]\) | \(107906079985/1372\) | \(18144700\) | \([]\) | \(103680\) | \(0.53875\) |
Rank
sage: E.rank()
The elliptic curves in class 185150bu have rank \(1\).
Complex multiplication
The elliptic curves in class 185150bu do not have complex multiplication.Modular form 185150.2.a.bu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.