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SageMath
E = EllipticCurve("ij1")
E.isogeny_class()
Elliptic curves in class 394944.ij
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
394944.ij1 | 394944ij1 | \([0, 1, 0, -69857, 3427455]\) | \(81182737/35904\) | \(16673964331892736\) | \([2]\) | \(2211840\) | \(1.8084\) | \(\Gamma_0(N)\)-optimal |
394944.ij2 | 394944ij2 | \([0, 1, 0, 239903, 25792127]\) | \(3288008303/2517768\) | \(-1169261748773978112\) | \([2]\) | \(4423680\) | \(2.1550\) |
Rank
sage: E.rank()
The elliptic curves in class 394944.ij have rank \(0\).
Complex multiplication
The elliptic curves in class 394944.ij do not have complex multiplication.Modular form 394944.2.a.ij
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.