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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 18150bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18150.bm4 | 18150bp1 | \([1, 0, 1, -366, 3628]\) | \(-24389/12\) | \(-2657341500\) | \([2]\) | \(11200\) | \(0.51368\) | \(\Gamma_0(N)\)-optimal |
| 18150.bm2 | 18150bp2 | \([1, 0, 1, -6416, 197228]\) | \(131872229/18\) | \(3986012250\) | \([2]\) | \(22400\) | \(0.86025\) | |
| 18150.bm3 | 18150bp3 | \([1, 0, 1, -3391, -365422]\) | \(-19465109/248832\) | \(-55102633344000\) | \([2]\) | \(56000\) | \(1.3184\) | |
| 18150.bm1 | 18150bp4 | \([1, 0, 1, -100191, -12175022]\) | \(502270291349/1889568\) | \(418435621956000\) | \([2]\) | \(112000\) | \(1.6650\) |
Rank
sage: E.rank()
The elliptic curves in class 18150bp have rank \(0\).
Complex multiplication
The elliptic curves in class 18150bp do not have complex multiplication.Modular form 18150.2.a.bp
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
