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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 131043r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 131043.n2 | 131043r1 | \([0, -1, 1, -15870763, -26229442713]\) | \(-5304438784000/497763387\) | \(-41485914271945103106267\) | \([]\) | \(7776000\) | \(3.0820\) | \(\Gamma_0(N)\)-optimal |
| 131043.n1 | 131043r2 | \([0, -1, 1, -1313196463, -18316069867140]\) | \(-3004935183806464000/2037123\) | \(-169783299347823716643\) | \([]\) | \(23328000\) | \(3.6313\) |
Rank
sage: E.rank()
The elliptic curves in class 131043r have rank \(1\).
Complex multiplication
The elliptic curves in class 131043r do not have complex multiplication.Modular form 131043.2.a.r
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.
