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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 59290.di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59290.di1 | 59290cv4 | \([1, -1, 1, -123970573, -531252109979]\) | \(1010962818911303721/57392720\) | \(11961927302181552080\) | \([2]\) | \(5898240\) | \(3.1273\) | |
| 59290.di2 | 59290cv3 | \([1, -1, 1, -12979693, 4247960357]\) | \(1160306142246441/634128110000\) | \(132166489967539201790000\) | \([2]\) | \(5898240\) | \(3.1273\) | |
| 59290.di3 | 59290cv2 | \([1, -1, 1, -7762173, -8267826619]\) | \(248158561089321/1859334400\) | \(387526901029352761600\) | \([2, 2]\) | \(2949120\) | \(2.7807\) | |
| 59290.di4 | 59290cv1 | \([1, -1, 1, -173053, -293179323]\) | \(-2749884201/176619520\) | \(-36811460728576737280\) | \([2]\) | \(1474560\) | \(2.4342\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59290.di have rank \(2\).
Complex multiplication
The elliptic curves in class 59290.di do not have complex multiplication.Modular form 59290.2.a.di
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
