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SageMath
E = EllipticCurve("kl1")
E.isogeny_class()
Elliptic curves in class 476850kl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
476850.kl2 | 476850kl1 | \([1, 0, 0, -74309488, -246165745408]\) | \(591139158854005457801/1097587482427392\) | \(84256989080715264000000\) | \([2]\) | \(104595456\) | \(3.2898\) | \(\Gamma_0(N)\)-optimal |
476850.kl1 | 476850kl2 | \([1, 0, 0, -1188421488, -15769088241408]\) | \(2418067440128989194388361/8359273562112\) | \(641704859541504000000\) | \([2]\) | \(209190912\) | \(3.6363\) |
Rank
sage: E.rank()
The elliptic curves in class 476850kl have rank \(0\).
Complex multiplication
The elliptic curves in class 476850kl do not have complex multiplication.Modular form 476850.2.a.kl
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.