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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 101478k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101478.k2 | 101478k1 | \([1, 0, 0, 8938334, 2268820292]\) | \(78975693098270145722349791/47925805879636550221824\) | \(-47925805879636550221824\) | \([7]\) | \(9985024\) | \(3.0412\) | \(\Gamma_0(N)\)-optimal |
101478.k1 | 101478k2 | \([1, 0, 0, -3334962226, -74128716508108]\) | \(-4102007684809181687432274264918049/3936639679171948631439024\) | \(-3936639679171948631439024\) | \([]\) | \(69895168\) | \(4.0142\) |
Rank
sage: E.rank()
The elliptic curves in class 101478k have rank \(0\).
Complex multiplication
The elliptic curves in class 101478k do not have complex multiplication.Modular form 101478.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.