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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 14490bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.bx1 | 14490bj1 | \([1, -1, 1, -11477, 467101]\) | \(8493409990827/185150000\) | \(3644307450000\) | \([2]\) | \(30720\) | \(1.1986\) | \(\Gamma_0(N)\)-optimal |
| 14490.bx2 | 14490bj2 | \([1, -1, 1, 943, 1415989]\) | \(4716275733/44023437500\) | \(-866513320312500\) | \([2]\) | \(61440\) | \(1.5452\) |
Rank
sage: E.rank()
The elliptic curves in class 14490bj have rank \(1\).
Complex multiplication
The elliptic curves in class 14490bj do not have complex multiplication.Modular form 14490.2.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.
