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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 60840bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60840.y2 | 60840bp1 | \([0, 0, 0, -29523, 4269278]\) | \(-1735192372/3796875\) | \(-6227071344000000\) | \([2]\) | \(460800\) | \(1.7194\) | \(\Gamma_0(N)\)-optimal |
| 60840.y1 | 60840bp2 | \([0, 0, 0, -614523, 185268278]\) | \(7824392006186/7381125\) | \(24210853385472000\) | \([2]\) | \(921600\) | \(2.0660\) |
Rank
sage: E.rank()
The elliptic curves in class 60840bp have rank \(0\).
Complex multiplication
The elliptic curves in class 60840bp do not have complex multiplication.Modular form 60840.2.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.
