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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 37026.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37026.x1 | 37026bn4 | \([1, -1, 1, -2109416, -1092378999]\) | \(803760366578833/65593817586\) | \(84712314376747902834\) | \([2]\) | \(1474560\) | \(2.5665\) | |
| 37026.x2 | 37026bn2 | \([1, -1, 1, -443246, 93934041]\) | \(7457162887153/1370924676\) | \(1770505306965703044\) | \([2, 2]\) | \(737280\) | \(2.2199\) | |
| 37026.x3 | 37026bn1 | \([1, -1, 1, -421466, 105416457]\) | \(6411014266033/296208\) | \(382543144161552\) | \([2]\) | \(368640\) | \(1.8734\) | \(\Gamma_0(N)\)-optimal |
| 37026.x4 | 37026bn3 | \([1, -1, 1, 874444, 545111097]\) | \(57258048889007/132611470002\) | \(-171263465829587365938\) | \([2]\) | \(1474560\) | \(2.5665\) |
Rank
sage: E.rank()
The elliptic curves in class 37026.x have rank \(1\).
Complex multiplication
The elliptic curves in class 37026.x do not have complex multiplication.Modular form 37026.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
