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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 190575.eh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190575.eh1 | 190575dx2 | \([1, -1, 0, -1815567, -899796034]\) | \(24642171/1225\) | \(32901659949301171875\) | \([2]\) | \(4866048\) | \(2.5040\) | |
190575.eh2 | 190575dx1 | \([1, -1, 0, -318192, 51037091]\) | \(132651/35\) | \(940047427122890625\) | \([2]\) | \(2433024\) | \(2.1574\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190575.eh have rank \(1\).
Complex multiplication
The elliptic curves in class 190575.eh do not have complex multiplication.Modular form 190575.2.a.eh
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.