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SageMath
E = EllipticCurve("io1")
E.isogeny_class()
Elliptic curves in class 381150.io
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381150.io1 | 381150io1 | \([1, -1, 1, -794630, 272788497]\) | \(74246873427/16940\) | \(12660571409062500\) | \([2]\) | \(5898240\) | \(2.0816\) | \(\Gamma_0(N)\)-optimal |
381150.io2 | 381150io2 | \([1, -1, 1, -703880, 337402497]\) | \(-51603494067/35870450\) | \(-26808759958689843750\) | \([2]\) | \(11796480\) | \(2.4281\) |
Rank
sage: E.rank()
The elliptic curves in class 381150.io have rank \(1\).
Complex multiplication
The elliptic curves in class 381150.io do not have complex multiplication.Modular form 381150.2.a.io
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.