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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 242592bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242592.bq3 | 242592bq1 | \([0, 1, 0, -5174, -133824]\) | \(5088448/441\) | \(1327822945344\) | \([2, 2]\) | \(442368\) | \(1.0670\) | \(\Gamma_0(N)\)-optimal |
| 242592.bq2 | 242592bq2 | \([0, 1, 0, -17809, 758207]\) | \(3241792/567\) | \(109260859502592\) | \([2]\) | \(884736\) | \(1.4136\) | |
| 242592.bq4 | 242592bq3 | \([0, 1, 0, 5656, -610344]\) | \(830584/7203\) | \(-173502198191616\) | \([2]\) | \(884736\) | \(1.4136\) | |
| 242592.bq1 | 242592bq4 | \([0, 1, 0, -80984, -8897460]\) | \(2438569736/21\) | \(505837312512\) | \([2]\) | \(884736\) | \(1.4136\) |
Rank
sage: E.rank()
The elliptic curves in class 242592bq have rank \(0\).
Complex multiplication
The elliptic curves in class 242592bq do not have complex multiplication.Modular form 242592.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
