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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 116242.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116242.k1 | 116242k2 | \([1, 1, 0, -689517, 219508205]\) | \(770616005574241/2349948272\) | \(110555386760667632\) | \([2]\) | \(3502080\) | \(2.1389\) | |
116242.k2 | 116242k1 | \([1, 1, 0, -25277, 6287165]\) | \(-37966934881/342216448\) | \(-16099874288850688\) | \([2]\) | \(1751040\) | \(1.7923\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116242.k have rank \(1\).
Complex multiplication
The elliptic curves in class 116242.k do not have complex multiplication.Modular form 116242.2.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.