Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 465690bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
465690.bw2 | 465690bw1 | \([1, 1, 1, -13545, -412905]\) | \(5841725401/1857600\) | \(87392428545600\) | \([2]\) | \(1886976\) | \(1.3790\) | \(\Gamma_0(N)\)-optimal* |
465690.bw1 | 465690bw2 | \([1, 1, 1, -85745, 9319655]\) | \(1481933914201/53916840\) | \(2536565238536040\) | \([2]\) | \(3773952\) | \(1.7255\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 465690bw have rank \(0\).
Complex multiplication
The elliptic curves in class 465690bw do not have complex multiplication.Modular form 465690.2.a.bw
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.