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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 8640bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8640.bc2 | 8640bj1 | \([0, 0, 0, 12, -8]\) | \(6912/5\) | \(-138240\) | \([]\) | \(1152\) | \(-0.32524\) | \(\Gamma_0(N)\)-optimal |
| 8640.bc1 | 8640bj2 | \([0, 0, 0, -228, -1352]\) | \(-5267712/125\) | \(-31104000\) | \([]\) | \(3456\) | \(0.22406\) |
Rank
sage: E.rank()
The elliptic curves in class 8640bj have rank \(0\).
Complex multiplication
The elliptic curves in class 8640bj do not have complex multiplication.Modular form 8640.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
