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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 63525bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63525.d2 | 63525bf1 | \([0, -1, 1, -105240758, 415585826468]\) | \(116423188793017446400/91315917\) | \(101107323272773125\) | \([]\) | \(6336000\) | \(3.0030\) | \(\Gamma_0(N)\)-optimal |
| 63525.d1 | 63525bf2 | \([0, -1, 1, -204333708, -480858845182]\) | \(1363413585016606720/644626239703677\) | \(446091681967064738201953125\) | \([]\) | \(31680000\) | \(3.8077\) |
Rank
sage: E.rank()
The elliptic curves in class 63525bf have rank \(0\).
Complex multiplication
The elliptic curves in class 63525bf do not have complex multiplication.Modular form 63525.2.a.bf
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
