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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 225400bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 225400.cs2 | 225400bj1 | \([0, -1, 0, -34708, -3186588]\) | \(-9826000/3703\) | \(-1742616988000000\) | \([2]\) | \(1105920\) | \(1.6343\) | \(\Gamma_0(N)\)-optimal |
| 225400.cs1 | 225400bj2 | \([0, -1, 0, -598208, -177871588]\) | \(12576878500/1127\) | \(2121446768000000\) | \([2]\) | \(2211840\) | \(1.9809\) |
Rank
sage: E.rank()
The elliptic curves in class 225400bj have rank \(1\).
Complex multiplication
The elliptic curves in class 225400bj do not have complex multiplication.Modular form 225400.2.a.bj
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.
