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SageMath
E = EllipticCurve("im1")
E.isogeny_class()
Elliptic curves in class 202800im
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202800.kf3 | 202800im1 | \([0, 1, 0, -470383, -124033012]\) | \(9538484224/26325\) | \(31766436731250000\) | \([2]\) | \(3096576\) | \(2.0394\) | \(\Gamma_0(N)\)-optimal |
| 202800.kf2 | 202800im2 | \([0, 1, 0, -660508, -14521012]\) | \(1650587344/950625\) | \(18353941222500000000\) | \([2, 2]\) | \(6193152\) | \(2.3859\) | |
| 202800.kf1 | 202800im3 | \([0, 1, 0, -6998008, 7096153988]\) | \(490757540836/2142075\) | \(165430190218800000000\) | \([2]\) | \(12386304\) | \(2.7325\) | |
| 202800.kf4 | 202800im4 | \([0, 1, 0, 2634992, -113386012]\) | \(26198797244/15234375\) | \(-1176534693750000000000\) | \([2]\) | \(12386304\) | \(2.7325\) |
Rank
sage: E.rank()
The elliptic curves in class 202800im have rank \(0\).
Complex multiplication
The elliptic curves in class 202800im do not have complex multiplication.Modular form 202800.2.a.im
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.
