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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 85176bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85176.cd1 | 85176bj1 | \([0, 0, 0, -14703, -681070]\) | \(10536048/91\) | \(3036024246528\) | \([2]\) | \(301056\) | \(1.2195\) | \(\Gamma_0(N)\)-optimal |
| 85176.cd2 | 85176bj2 | \([0, 0, 0, -4563, -1603810]\) | \(-78732/8281\) | \(-1105112825736192\) | \([2]\) | \(602112\) | \(1.5661\) |
Rank
sage: E.rank()
The elliptic curves in class 85176bj have rank \(0\).
Complex multiplication
The elliptic curves in class 85176bj do not have complex multiplication.Modular form 85176.2.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.
