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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 28594.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28594.e1 | 28594f4 | \([1, 1, 0, -95050, -7833894]\) | \(159661140625/48275138\) | \(28715177906893298\) | \([2]\) | \(302400\) | \(1.8631\) | |
28594.e2 | 28594f3 | \([1, 1, 0, -86640, -9850612]\) | \(120920208625/19652\) | \(11689467904292\) | \([2]\) | \(151200\) | \(1.5166\) | |
28594.e3 | 28594f2 | \([1, 1, 0, -36180, 2633192]\) | \(8805624625/2312\) | \(1375231518152\) | \([2]\) | \(100800\) | \(1.3138\) | |
28594.e4 | 28594f1 | \([1, 1, 0, -2540, 29456]\) | \(3048625/1088\) | \(647167773248\) | \([2]\) | \(50400\) | \(0.96726\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28594.e have rank \(0\).
Complex multiplication
The elliptic curves in class 28594.e do not have complex multiplication.Modular form 28594.2.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 LMFDB 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 LMFDB labels.