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SageMath
E = EllipticCurve("fp1")
E.isogeny_class()
Elliptic curves in class 185130fp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185130.v2 | 185130fp1 | \([1, -1, 0, 2040, -33984]\) | \(287306415693/314432000\) | \(-1027249344000\) | \([]\) | \(248832\) | \(0.99139\) | \(\Gamma_0(N)\)-optimal |
| 185130.v1 | 185130fp2 | \([1, -1, 0, -20400, 1655000]\) | \(-394229869803/265625000\) | \(-632623921875000\) | \([]\) | \(746496\) | \(1.5407\) |
Rank
sage: E.rank()
The elliptic curves in class 185130fp have rank \(0\).
Complex multiplication
The elliptic curves in class 185130fp do not have complex multiplication.Modular form 185130.2.a.fp
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
