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SageMath
E = EllipticCurve("he1")
E.isogeny_class()
Elliptic curves in class 297024he
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 297024.he3 | 297024he1 | \([0, 1, 0, -55777, -5088865]\) | \(73207745356537/668304\) | \(175191883776\) | \([2]\) | \(737280\) | \(1.3219\) | \(\Gamma_0(N)\)-optimal |
| 297024.he2 | 297024he2 | \([0, 1, 0, -57057, -4844385]\) | \(78364289651257/6978597444\) | \(1829397448359936\) | \([2, 2]\) | \(1474560\) | \(1.6685\) | |
| 297024.he1 | 297024he3 | \([0, 1, 0, -198497, 28507167]\) | \(3299497626614617/563987509722\) | \(147845941748563968\) | \([4]\) | \(2949120\) | \(2.0151\) | |
| 297024.he4 | 297024he4 | \([0, 1, 0, 63903, -22528737]\) | \(110088190986983/901697560218\) | \(-236374605225787392\) | \([2]\) | \(2949120\) | \(2.0151\) |
Rank
sage: E.rank()
The elliptic curves in class 297024he have rank \(0\).
Complex multiplication
The elliptic curves in class 297024he do not have complex multiplication.Modular form 297024.2.a.he
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.
