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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 55470.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55470.x1 | 55470bd4 | \([1, 1, 1, -1550425, -738640015]\) | \(65202655558249/512820150\) | \(3241722346992637350\) | \([2]\) | \(1419264\) | \(2.3801\) | |
| 55470.x2 | 55470bd2 | \([1, 1, 1, -163675, 6322085]\) | \(76711450249/41602500\) | \(262984506246022500\) | \([2, 2]\) | \(709632\) | \(2.0335\) | |
| 55470.x3 | 55470bd1 | \([1, 1, 1, -126695, 17282957]\) | \(35578826569/51600\) | \(326182333328400\) | \([4]\) | \(354816\) | \(1.6869\) | \(\Gamma_0(N)\)-optimal |
| 55470.x4 | 55470bd3 | \([1, 1, 1, 631395, 50527977]\) | \(4403686064471/2721093750\) | \(-17201021484114843750\) | \([2]\) | \(1419264\) | \(2.3801\) |
Rank
sage: E.rank()
The elliptic curves in class 55470.x have rank \(0\).
Complex multiplication
The elliptic curves in class 55470.x do not have complex multiplication.Modular form 55470.2.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.
