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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 92736.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92736.ce1 | 92736ei4 | \([0, 0, 0, -873498540, -9888499236656]\) | \(385693937170561837203625/2159357734550274048\) | \(412659689321175392188366848\) | \([2]\) | \(44236800\) | \(3.9494\) | |
| 92736.ce2 | 92736ei2 | \([0, 0, 0, -64509420, 190007883088]\) | \(155355156733986861625/8291568305839392\) | \(1584543378953185989230592\) | \([2]\) | \(14745600\) | \(3.4001\) | |
| 92736.ce3 | 92736ei3 | \([0, 0, 0, -24151980, -325876186928]\) | \(-8152944444844179625/235342826399858688\) | \(-44974714505264361256255488\) | \([2]\) | \(22118400\) | \(3.6028\) | |
| 92736.ce4 | 92736ei1 | \([0, 0, 0, 2675220, 11861091664]\) | \(11079872671250375/324440155855872\) | \(-62001479317960966275072\) | \([2]\) | \(7372800\) | \(3.0535\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92736.ce have rank \(2\).
Complex multiplication
The elliptic curves in class 92736.ce do not have complex multiplication.Modular form 92736.2.a.ce
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
