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SageMath
E = EllipticCurve("jo1")
E.isogeny_class()
Elliptic curves in class 142800.jo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142800.jo1 | 142800cd2 | \([0, 1, 0, -18368, 5663028]\) | \(-6693187811305/131714173248\) | \(-13487531340595200\) | \([]\) | \(933120\) | \(1.7760\) | |
| 142800.jo2 | 142800cd1 | \([0, 1, 0, 2032, -204012]\) | \(9056932295/181997172\) | \(-18636510412800\) | \([]\) | \(311040\) | \(1.2267\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 142800.jo have rank \(0\).
Complex multiplication
The elliptic curves in class 142800.jo do not have complex multiplication.Modular form 142800.2.a.jo
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
