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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 155610bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155610.db1 | 155610bp1 | \([1, -1, 1, -433508, -109751673]\) | \(12359092816971484921/116188800000\) | \(84701635200000\) | \([2]\) | \(2048000\) | \(1.8354\) | \(\Gamma_0(N)\)-optimal |
155610.db2 | 155610bp2 | \([1, -1, 1, -423428, -115106169]\) | \(-11516856136356002041/1201114687500000\) | \(-875612607187500000\) | \([2]\) | \(4096000\) | \(2.1819\) |
Rank
sage: E.rank()
The elliptic curves in class 155610bp have rank \(0\).
Complex multiplication
The elliptic curves in class 155610bp do not have complex multiplication.Modular form 155610.2.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.