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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 90354i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
90354.j2 | 90354i1 | \([1, 0, 1, -82938156, 136420743274]\) | \(24591016773082896625/11097062309363712\) | \(28472025829453003864670208\) | \([2]\) | \(28892160\) | \(3.5795\) | \(\Gamma_0(N)\)-optimal |
90354.j1 | 90354i2 | \([1, 0, 1, -1120311596, 14425617455210]\) | \(60607987148648054544625/35377817158176768\) | \(90769799775507463947866112\) | \([2]\) | \(57784320\) | \(3.9261\) |
Rank
sage: E.rank()
The elliptic curves in class 90354i have rank \(0\).
Complex multiplication
The elliptic curves in class 90354i do not have complex multiplication.Modular form 90354.2.a.i
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.