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SageMath
E = EllipticCurve("nr1")
E.isogeny_class()
Elliptic curves in class 187200nr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.nb2 | 187200nr1 | \([0, 0, 0, 1725, 42500]\) | \(778688/1521\) | \(-1108809000000\) | \([2]\) | \(262144\) | \(0.99573\) | \(\Gamma_0(N)\)-optimal |
187200.nb1 | 187200nr2 | \([0, 0, 0, -12900, 452000]\) | \(5088448/1053\) | \(49128768000000\) | \([2]\) | \(524288\) | \(1.3423\) |
Rank
sage: E.rank()
The elliptic curves in class 187200nr have rank \(0\).
Complex multiplication
The elliptic curves in class 187200nr do not have complex multiplication.Modular form 187200.2.a.nr
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 Cremona 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 Cremona labels.