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SageMath
E = EllipticCurve("fj1")
E.isogeny_class()
Elliptic curves in class 154560fj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
154560.ge1 | 154560fj1 | \([0, 1, 0, -15681, 716319]\) | \(1626794704081/83462400\) | \(21879167385600\) | \([2]\) | \(589824\) | \(1.3176\) | \(\Gamma_0(N)\)-optimal |
154560.ge2 | 154560fj2 | \([0, 1, 0, 9919, 2851359]\) | \(411664745519/13605414480\) | \(-3566577773445120\) | \([2]\) | \(1179648\) | \(1.6642\) |
Rank
sage: E.rank()
The elliptic curves in class 154560fj have rank \(0\).
Complex multiplication
The elliptic curves in class 154560fj do not have complex multiplication.Modular form 154560.2.a.fj
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.