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SageMath
E = EllipticCurve("hu1")
E.isogeny_class()
Elliptic curves in class 382200hu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 382200.hu4 | 382200hu1 | \([0, 1, 0, -2811783, 1529053938]\) | \(83587439220736/13990184325\) | \(411482798912981250000\) | \([2]\) | \(10616832\) | \(2.6766\) | \(\Gamma_0(N)\)-optimal |
| 382200.hu2 | 382200hu2 | \([0, 1, 0, -42997908, 108504518688]\) | \(18681746265374416/693005625\) | \(326125675102500000000\) | \([2, 2]\) | \(21233664\) | \(3.0232\) | |
| 382200.hu1 | 382200hu3 | \([0, 1, 0, -687960408, 6945107018688]\) | \(19129597231400697604/26325\) | \(49553758800000000\) | \([2]\) | \(42467328\) | \(3.3698\) | |
| 382200.hu3 | 382200hu4 | \([0, 1, 0, -41013408, 118974740688]\) | \(-4053153720264484/903687890625\) | \(-1701087626306250000000000\) | \([2]\) | \(42467328\) | \(3.3698\) |
Rank
sage: E.rank()
The elliptic curves in class 382200hu have rank \(1\).
Complex multiplication
The elliptic curves in class 382200hu do not have complex multiplication.Modular form 382200.2.a.hu
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.
