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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 286110e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286110.e3 | 286110e1 | \([1, -1, 0, -104731920, -389747116800]\) | \(7220044159551112609/448454983680000\) | \(7891142958626038087680000\) | \([2]\) | \(91750400\) | \(3.5288\) | \(\Gamma_0(N)\)-optimal |
| 286110.e2 | 286110e2 | \([1, -1, 0, -317805840, 1700891571456]\) | \(201738262891771037089/45727545600000000\) | \(804635052810951225600000000\) | \([2, 2]\) | \(183500800\) | \(3.8754\) | |
| 286110.e1 | 286110e3 | \([1, -1, 0, -4767388560, 126690560092800]\) | \(680995599504466943307169/52207031250000000\) | \(918649947110800781250000000\) | \([2]\) | \(367001600\) | \(4.2220\) | |
| 286110.e4 | 286110e4 | \([1, -1, 0, 722594160, 10509542211456]\) | \(2371297246710590562911/4084000833203280000\) | \(-71863254040568711617187280000\) | \([2]\) | \(367001600\) | \(4.2220\) |
Rank
sage: E.rank()
The elliptic curves in class 286110e have rank \(0\).
Complex multiplication
The elliptic curves in class 286110e do not have complex multiplication.Modular form 286110.2.a.e
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
