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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 35280.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.co1 | 35280dd1 | \([0, 0, 0, -4017363, 3092575122]\) | \(551105805571803/1376829440\) | \(17913980449739243520\) | \([2]\) | \(1290240\) | \(2.5717\) | \(\Gamma_0(N)\)-optimal |
35280.co2 | 35280dd2 | \([0, 0, 0, -2512083, 5438102418]\) | \(-134745327251163/903920796800\) | \(-11760948024170604134400\) | \([2]\) | \(2580480\) | \(2.9183\) |
Rank
sage: E.rank()
The elliptic curves in class 35280.co have rank \(1\).
Complex multiplication
The elliptic curves in class 35280.co do not have complex multiplication.Modular form 35280.2.a.co
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.