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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 25168bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25168.bm2 | 25168bp1 | \([0, 0, 0, -5203, 220946]\) | \(-2146689/1664\) | \(-12074506256384\) | \([]\) | \(67200\) | \(1.2089\) | \(\Gamma_0(N)\)-optimal |
| 25168.bm1 | 25168bp2 | \([0, 0, 0, -411763, -111583054]\) | \(-1064019559329/125497034\) | \(-910645866701103104\) | \([]\) | \(470400\) | \(2.1819\) |
Rank
sage: E.rank()
The elliptic curves in class 25168bp have rank \(0\).
Complex multiplication
The elliptic curves in class 25168bp do not have complex multiplication.Modular form 25168.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
