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SageMath
E = EllipticCurve("hi1")
E.isogeny_class()
Elliptic curves in class 254800hi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254800.hi2 | 254800hi1 | \([0, -1, 0, -637408, 194925312]\) | \(3803721481/26000\) | \(195767936000000000\) | \([2]\) | \(3981312\) | \(2.1520\) | \(\Gamma_0(N)\)-optimal |
| 254800.hi3 | 254800hi2 | \([0, -1, 0, -245408, 431693312]\) | \(-217081801/10562500\) | \(-79530724000000000000\) | \([2]\) | \(7962624\) | \(2.4985\) | |
| 254800.hi1 | 254800hi3 | \([0, -1, 0, -4067408, -3029274688]\) | \(988345570681/44994560\) | \(338788159324160000000\) | \([2]\) | \(11943936\) | \(2.7013\) | |
| 254800.hi4 | 254800hi4 | \([0, -1, 0, 2204592, -11534106688]\) | \(157376536199/7722894400\) | \(-58149811408998400000000\) | \([2]\) | \(23887872\) | \(3.0478\) |
Rank
sage: E.rank()
The elliptic curves in class 254800hi have rank \(0\).
Complex multiplication
The elliptic curves in class 254800hi do not have complex multiplication.Modular form 254800.2.a.hi
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
