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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 273273.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273273.q1 | 273273q1 | \([1, 0, 0, -158103, -24146760]\) | \(263991523375/797511\) | \(1320355612432857\) | \([2]\) | \(1354752\) | \(1.7703\) | \(\Gamma_0(N)\)-optimal |
273273.q2 | 273273q2 | \([1, 0, 0, -93038, -44173767]\) | \(-53796109375/477854091\) | \(-791133076504087317\) | \([2]\) | \(2709504\) | \(2.1169\) |
Rank
sage: E.rank()
The elliptic curves in class 273273.q have rank \(0\).
Complex multiplication
The elliptic curves in class 273273.q do not have complex multiplication.Modular form 273273.2.a.q
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.