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SageMath
E = EllipticCurve("fa1")
E.isogeny_class()
Elliptic curves in class 193600fa
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193600.ix4 | 193600fa1 | \([0, -1, 0, -548533, 153346437]\) | \(643956736/15125\) | \(428717762000000000\) | \([2]\) | \(3317760\) | \(2.1688\) | \(\Gamma_0(N)\)-optimal |
| 193600.ix3 | 193600fa2 | \([0, -1, 0, -1214033, -290542063]\) | \(436334416/171875\) | \(77948684000000000000\) | \([2]\) | \(6635520\) | \(2.5154\) | |
| 193600.ix2 | 193600fa3 | \([0, -1, 0, -5388533, -4751993563]\) | \(610462990336/8857805\) | \(251074270137680000000\) | \([2]\) | \(9953280\) | \(2.7181\) | |
| 193600.ix1 | 193600fa4 | \([0, -1, 0, -85914033, -306481042063]\) | \(154639330142416/33275\) | \(15090865222400000000\) | \([2]\) | \(19906560\) | \(3.0647\) |
Rank
sage: E.rank()
The elliptic curves in class 193600fa have rank \(1\).
Complex multiplication
The elliptic curves in class 193600fa do not have complex multiplication.Modular form 193600.2.a.fa
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.
