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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 190575.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190575.t1 | 190575bq2 | \([1, -1, 1, -15005, 680122]\) | \(24642171/1225\) | \(18572129296875\) | \([2]\) | \(442368\) | \(1.3050\) | |
190575.t2 | 190575bq1 | \([1, -1, 1, -2630, -37628]\) | \(132651/35\) | \(530632265625\) | \([2]\) | \(221184\) | \(0.95843\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190575.t have rank \(2\).
Complex multiplication
The elliptic curves in class 190575.t do not have complex multiplication.Modular form 190575.2.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.