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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 19350bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19350.cs4 | 19350bq1 | \([1, -1, 1, -174230, 21791397]\) | \(1386456968640843/318028000000\) | \(134168062500000000\) | \([2]\) | \(221184\) | \(1.9989\) | \(\Gamma_0(N)\)-optimal |
| 19350.cs3 | 19350bq2 | \([1, -1, 1, -924230, -323208603]\) | \(206956783279200843/12642726098000\) | \(5333650072593750000\) | \([2]\) | \(442368\) | \(2.3454\) | |
| 19350.cs2 | 19350bq3 | \([1, -1, 1, -4608605, -3805208603]\) | \(35198225176082067/18035507200\) | \(5546763878400000000\) | \([2]\) | \(663552\) | \(2.5482\) | |
| 19350.cs1 | 19350bq4 | \([1, -1, 1, -73728605, -243651608603]\) | \(144118734029937784467/37867520\) | \(11646037440000000\) | \([2]\) | \(1327104\) | \(2.8947\) |
Rank
sage: E.rank()
The elliptic curves in class 19350bq have rank \(0\).
Complex multiplication
The elliptic curves in class 19350bq do not have complex multiplication.Modular form 19350.2.a.bq
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.
