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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 92400bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.p2 | 92400bf1 | \([0, -1, 0, -19431083, 37029483162]\) | \(-25963589461091772416/3923372657421063\) | \(-122605395544408218750000\) | \([2]\) | \(8064000\) | \(3.1597\) | \(\Gamma_0(N)\)-optimal |
| 92400.p1 | 92400bf2 | \([0, -1, 0, -321401708, 2217861336912]\) | \(7343418009347613339536/136478763980097\) | \(68239381990048500000000\) | \([2]\) | \(16128000\) | \(3.5063\) |
Rank
sage: E.rank()
The elliptic curves in class 92400bf have rank \(0\).
Complex multiplication
The elliptic curves in class 92400bf do not have complex multiplication.Modular form 92400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
