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SageMath
E = EllipticCurve("io1")
E.isogeny_class()
Elliptic curves in class 271950.io
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 271950.io1 | 271950io4 | \([1, 0, 0, -12847213, 7910558417]\) | \(127568139540190201/59114336463360\) | \(108667852665278760000000\) | \([2]\) | \(41803776\) | \(3.1148\) | |
| 271950.io2 | 271950io2 | \([1, 0, 0, -6507838, -6390244708]\) | \(16581570075765001/998001000\) | \(1834590932015625000\) | \([2]\) | \(13934592\) | \(2.5655\) | |
| 271950.io3 | 271950io1 | \([1, 0, 0, -382838, -112119708]\) | \(-3375675045001/999000000\) | \(-1836427359375000000\) | \([2]\) | \(6967296\) | \(2.2189\) | \(\Gamma_0(N)\)-optimal |
| 271950.io4 | 271950io3 | \([1, 0, 0, 2832787, 932958417]\) | \(1367594037332999/995878502400\) | \(-1830689217638400000000\) | \([2]\) | \(20901888\) | \(2.7682\) |
Rank
sage: E.rank()
The elliptic curves in class 271950.io have rank \(0\).
Complex multiplication
The elliptic curves in class 271950.io do not have complex multiplication.Modular form 271950.2.a.io
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
