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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 327990j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
327990.j1 | 327990j1 | \([1, 1, 0, -1602122, -762195756]\) | \(764579942079121/21285239040\) | \(12660956574051651840\) | \([2]\) | \(11612160\) | \(2.4447\) | \(\Gamma_0(N)\)-optimal |
327990.j2 | 327990j2 | \([1, 1, 0, 348998, -2497521884]\) | \(7903193128559/4535269736400\) | \(-2697684206236242584400\) | \([2]\) | \(23224320\) | \(2.7913\) |
Rank
sage: E.rank()
The elliptic curves in class 327990j have rank \(0\).
Complex multiplication
The elliptic curves in class 327990j do not have complex multiplication.Modular form 327990.2.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.