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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 57498t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57498.u2 | 57498t1 | \([1, 0, 0, 1681788, 447298560]\) | \(205034573717063/152320630896\) | \(-390813065325408532464\) | \([2]\) | \(2757888\) | \(2.6395\) | \(\Gamma_0(N)\)-optimal |
57498.u1 | 57498t2 | \([1, 0, 0, -7709552, 3811276548]\) | \(19751532485554297/8983697617692\) | \(23049710228182750028028\) | \([2]\) | \(5515776\) | \(2.9860\) |
Rank
sage: E.rank()
The elliptic curves in class 57498t have rank \(0\).
Complex multiplication
The elliptic curves in class 57498t do not have complex multiplication.Modular form 57498.2.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 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.