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SageMath
E = EllipticCurve("fu1")
E.isogeny_class()
Elliptic curves in class 304200.fu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 304200.fu1 | 304200fu3 | \([0, 0, 0, -21354852675, 1201138210736750]\) | \(19129597231400697604/26325\) | \(1482094872133200000000\) | \([2]\) | \(198180864\) | \(4.2286\) | |
| 304200.fu2 | 304200fu2 | \([0, 0, 0, -1334690175, 18767433649250]\) | \(18681746265374416/693005625\) | \(9754036877226622500000000\) | \([2, 2]\) | \(99090432\) | \(3.8820\) | |
| 304200.fu3 | 304200fu4 | \([0, 0, 0, -1273089675, 20578057145750]\) | \(-4053153720264484/903687890625\) | \(-50877538032447506250000000000\) | \([2]\) | \(198180864\) | \(4.2286\) | |
| 304200.fu4 | 304200fu1 | \([0, 0, 0, -87280050, 264599265125]\) | \(83587439220736/13990184325\) | \(12306968452208436581250000\) | \([2]\) | \(49545216\) | \(3.5355\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 304200.fu have rank \(1\).
Complex multiplication
The elliptic curves in class 304200.fu do not have complex multiplication.Modular form 304200.2.a.fu
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.
