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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 374790cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374790.cn3 | 374790cn1 | \([1, 1, 1, -5786, -1089817]\) | \(-24137569/561600\) | \(-498422067249600\) | \([2]\) | \(1451520\) | \(1.5009\) | \(\Gamma_0(N)\)-optimal |
374790.cn2 | 374790cn2 | \([1, 1, 1, -197986, -33840697]\) | \(967068262369/4928040\) | \(4373653640115240\) | \([2]\) | \(2903040\) | \(1.8475\) | |
374790.cn4 | 374790cn3 | \([1, 1, 1, 51874, 28754999]\) | \(17394111071/411937500\) | \(-365596047591937500\) | \([2]\) | \(4354560\) | \(2.0502\) | |
374790.cn1 | 374790cn4 | \([1, 1, 1, -1149376, 449672999]\) | \(189208196468929/10860320250\) | \(9638574198713840250\) | \([2]\) | \(8709120\) | \(2.3968\) |
Rank
sage: E.rank()
The elliptic curves in class 374790cn have rank \(1\).
Complex multiplication
The elliptic curves in class 374790cn do not have complex multiplication.Modular form 374790.2.a.cn
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.