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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 88935.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88935.k1 | 88935n1 | \([1, 1, 1, -23416, 1363088]\) | \(2336752783/12375\) | \(7519612109625\) | \([2]\) | \(230400\) | \(1.3154\) | \(\Gamma_0(N)\)-optimal |
88935.k2 | 88935n2 | \([1, 1, 1, -10711, 2852114]\) | \(-223648543/5671875\) | \(-3446488883578125\) | \([2]\) | \(460800\) | \(1.6620\) |
Rank
sage: E.rank()
The elliptic curves in class 88935.k have rank \(1\).
Complex multiplication
The elliptic curves in class 88935.k do not have complex multiplication.Modular form 88935.2.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 LMFDB 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 LMFDB labels.