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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 38720bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38720.n2 | 38720bb1 | \([0, 1, 0, -1595425, 1154549823]\) | \(-726572699/512000\) | \(-316478381828866048000\) | \([2]\) | \(1520640\) | \(2.6337\) | \(\Gamma_0(N)\)-optimal |
38720.n1 | 38720bb2 | \([0, 1, 0, -28854305, 59635750975]\) | \(4298149261979/1000000\) | \(618121839509504000000\) | \([2]\) | \(3041280\) | \(2.9802\) |
Rank
sage: E.rank()
The elliptic curves in class 38720bb have rank \(0\).
Complex multiplication
The elliptic curves in class 38720bb do not have complex multiplication.Modular form 38720.2.a.bb
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.