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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 364650.cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.cq1 | 364650cq2 | \([1, 0, 1, -773076, 255981298]\) | \(26161307059325381/638952448992\) | \(1247954001937500000\) | \([2]\) | \(7219200\) | \(2.2564\) | |
364650.cq2 | 364650cq1 | \([1, 0, 1, 6924, 12621298]\) | \(18799877179/35241643008\) | \(-68831334000000000\) | \([2]\) | \(3609600\) | \(1.9098\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 364650.cq have rank \(1\).
Complex multiplication
The elliptic curves in class 364650.cq do not have complex multiplication.Modular form 364650.2.a.cq
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.