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SageMath
E = EllipticCurve("jo1")
E.isogeny_class()
Elliptic curves in class 428400.jo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
428400.jo1 | 428400jo2 | \([0, 0, 0, -1373475, 619465250]\) | \(6141556990297/1019592\) | \(47570084352000000\) | \([2]\) | \(4718592\) | \(2.2081\) | \(\Gamma_0(N)\)-optimal* |
428400.jo2 | 428400jo1 | \([0, 0, 0, -77475, 11641250]\) | \(-1102302937/616896\) | \(-28781899776000000\) | \([2]\) | \(2359296\) | \(1.8615\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 428400.jo have rank \(1\).
Complex multiplication
The elliptic curves in class 428400.jo do not have complex multiplication.Modular form 428400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.