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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 90354.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
90354.t1 | 90354x1 | \([1, 0, 0, -50578418, 133339353924]\) | \(5577108481460841625/233729407061568\) | \(599685712257776106549312\) | \([2]\) | \(17335296\) | \(3.3274\) | \(\Gamma_0(N)\)-optimal |
90354.t2 | 90354x2 | \([1, 0, 0, 24388022, 494812534316]\) | \(625234740274982375/41585929145369928\) | \(-106698116651078424344028552\) | \([2]\) | \(34670592\) | \(3.6739\) |
Rank
sage: E.rank()
The elliptic curves in class 90354.t have rank \(1\).
Complex multiplication
The elliptic curves in class 90354.t do not have complex multiplication.Modular form 90354.2.a.t
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.