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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 185150.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185150.p1 | 185150cd1 | \([1, -1, 0, -17823167, -9568454259]\) | \(270701905514769/139540889600\) | \(322766556934169600000000\) | \([2]\) | \(19464192\) | \(3.2030\) | \(\Gamma_0(N)\)-optimal |
| 185150.p2 | 185150cd2 | \([1, -1, 0, 66816833, -74318054259]\) | \(14262456319278831/9284810958080\) | \(-21476331943379914580000000\) | \([2]\) | \(38928384\) | \(3.5496\) |
Rank
sage: E.rank()
The elliptic curves in class 185150.p have rank \(0\).
Complex multiplication
The elliptic curves in class 185150.p do not have complex multiplication.Modular form 185150.2.a.p
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.
