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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 26010v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26010.r1 | 26010v1 | \([1, -1, 0, -104094, -16137900]\) | \(-24529249/8000\) | \(-40682617395912000\) | \([]\) | \(220320\) | \(1.8996\) | \(\Gamma_0(N)\)-optimal |
| 26010.r2 | 26010v2 | \([1, -1, 0, 780246, 146757528]\) | \(10329972191/7812500\) | \(-39729118550695312500\) | \([3]\) | \(660960\) | \(2.4489\) |
Rank
sage: E.rank()
The elliptic curves in class 26010v have rank \(0\).
Complex multiplication
The elliptic curves in class 26010v do not have complex multiplication.Modular form 26010.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
