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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 160446bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160446.c2 | 160446bp1 | \([1, 1, 0, -137700, -18064944]\) | \(162995025390625/15251079168\) | \(27018217061941248\) | \([2]\) | \(1433600\) | \(1.8913\) | \(\Gamma_0(N)\)-optimal |
| 160446.c1 | 160446bp2 | \([1, 1, 0, -2151140, -1215256368]\) | \(621403856941038625/6310317312\) | \(11179112047564032\) | \([2]\) | \(2867200\) | \(2.2379\) |
Rank
sage: E.rank()
The elliptic curves in class 160446bp have rank \(1\).
Complex multiplication
The elliptic curves in class 160446bp do not have complex multiplication.Modular form 160446.2.a.bp
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.
