Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 8470.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8470.z1 | 8470ba4 | \([1, -1, 1, -2530012, 1549562831]\) | \(1010962818911303721/57392720\) | \(101674704435920\) | \([2]\) | \(122880\) | \(2.1543\) | |
| 8470.z2 | 8470ba3 | \([1, -1, 1, -264892, -12309041]\) | \(1160306142246441/634128110000\) | \(1123396628679710000\) | \([2]\) | \(122880\) | \(2.1543\) | |
| 8470.z3 | 8470ba2 | \([1, -1, 1, -158412, 24149711]\) | \(248158561089321/1859334400\) | \(3293924308998400\) | \([2, 2]\) | \(61440\) | \(1.8078\) | |
| 8470.z4 | 8470ba1 | \([1, -1, 1, -3532, 855759]\) | \(-2749884201/176619520\) | \(-312892253470720\) | \([4]\) | \(30720\) | \(1.4612\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8470.z have rank \(0\).
Complex multiplication
The elliptic curves in class 8470.z do not have complex multiplication.Modular form 8470.2.a.z
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.
