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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 433200j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
433200.j2 | 433200j1 | \([0, -1, 0, 168467, -5422688]\) | \(44957696/27075\) | \(-318441807018750000\) | \([2]\) | \(6635520\) | \(2.0478\) | \(\Gamma_0(N)\)-optimal* |
433200.j1 | 433200j2 | \([0, -1, 0, -688908, -43147188]\) | \(192143824/106875\) | \(20112114127500000000\) | \([2]\) | \(13271040\) | \(2.3944\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 433200j have rank \(1\).
Complex multiplication
The elliptic curves in class 433200j do not have complex multiplication.Modular form 433200.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.