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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 296208.et
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296208.et1 | 296208et4 | \([0, 0, 0, -27639804819, -1768685320911278]\) | \(441453577446719855661097/4354701912\) | \(23035732106817768357888\) | \([2]\) | \(247726080\) | \(4.3227\) | |
| 296208.et2 | 296208et2 | \([0, 0, 0, -1727528979, -27634324766510]\) | \(107784459654566688937/10704361149504\) | \(56624494809876218828292096\) | \([2, 2]\) | \(123863040\) | \(3.9762\) | |
| 296208.et3 | 296208et3 | \([0, 0, 0, -1597197459, -31979707974830]\) | \(-85183593440646799657/34223681512621656\) | \(-181038237510894952201161375744\) | \([2]\) | \(247726080\) | \(4.3227\) | |
| 296208.et4 | 296208et1 | \([0, 0, 0, -116157459, -362506339118]\) | \(32765849647039657/8229948198912\) | \(43535214532297067109285888\) | \([2]\) | \(61931520\) | \(3.6296\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 296208.et have rank \(0\).
Complex multiplication
The elliptic curves in class 296208.et do not have complex multiplication.Modular form 296208.2.a.et
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.
