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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 17136x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17136.be2 | 17136x1 | \([0, 0, 0, -3099, 93130]\) | \(-1102302937/616896\) | \(-1842041585664\) | \([2]\) | \(18432\) | \(1.0568\) | \(\Gamma_0(N)\)-optimal |
17136.be1 | 17136x2 | \([0, 0, 0, -54939, 4955722]\) | \(6141556990297/1019592\) | \(3044485398528\) | \([2]\) | \(36864\) | \(1.4034\) |
Rank
sage: E.rank()
The elliptic curves in class 17136x have rank \(1\).
Complex multiplication
The elliptic curves in class 17136x do not have complex multiplication.Modular form 17136.2.a.x
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.