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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 106470.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106470.co1 | 106470p1 | \([1, -1, 0, -7793889, -8354851075]\) | \(551105805571803/1376829440\) | \(130807170052950343680\) | \([2]\) | \(6451200\) | \(2.7374\) | \(\Gamma_0(N)\)-optimal |
| 106470.co2 | 106470p2 | \([1, -1, 0, -4873569, -14693697667]\) | \(-134745327251163/903920796800\) | \(-85877972932810016649600\) | \([2]\) | \(12902400\) | \(3.0840\) |
Rank
sage: E.rank()
The elliptic curves in class 106470.co have rank \(1\).
Complex multiplication
The elliptic curves in class 106470.co do not have complex multiplication.Modular form 106470.2.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.
