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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 87120bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.h3 | 87120bn1 | \([0, 0, 0, -3719298, -2759544997]\) | \(275361373935616/148240125\) | \(3063157970528898000\) | \([2]\) | \(2949120\) | \(2.4963\) | \(\Gamma_0(N)\)-optimal |
| 87120.h2 | 87120bn2 | \([0, 0, 0, -4378143, -1714485058]\) | \(28071778927696/12404390625\) | \(4101087530790756000000\) | \([2, 2]\) | \(5898240\) | \(2.8429\) | |
| 87120.h4 | 87120bn3 | \([0, 0, 0, 15027837, -12772012462]\) | \(283811208976796/217529296875\) | \(-287674490094750000000000\) | \([2]\) | \(11796480\) | \(3.1894\) | |
| 87120.h1 | 87120bn4 | \([0, 0, 0, -34325643, 76226878442]\) | \(3382175663521924/59189241375\) | \(78275593569507345792000\) | \([2]\) | \(11796480\) | \(3.1894\) |
Rank
sage: E.rank()
The elliptic curves in class 87120bn have rank \(1\).
Complex multiplication
The elliptic curves in class 87120bn do not have complex multiplication.Modular form 87120.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
