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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 3150.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3150.bn1 | 3150bd2 | \([1, -1, 1, -4604555, -3801870053]\) | \(280844088456303/614656\) | \(23629441500000000\) | \([2]\) | \(92160\) | \(2.3881\) | |
| 3150.bn2 | 3150bd1 | \([1, -1, 1, -284555, -60750053]\) | \(-66282611823/3211264\) | \(-123451776000000000\) | \([2]\) | \(46080\) | \(2.0416\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3150.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 3150.bn do not have complex multiplication.Modular form 3150.2.a.bn
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 LMFDB 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 LMFDB labels.
