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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 7056.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7056.bq1 | 7056w3 | \([0, 0, 0, -1778259, -912726430]\) | \(7080974546692/189\) | \(16598831993856\) | \([2]\) | \(73728\) | \(2.0504\) | |
| 7056.bq2 | 7056w4 | \([0, 0, 0, -173019, 3322298]\) | \(6522128932/3720087\) | \(326714810135067648\) | \([2]\) | \(73728\) | \(2.0504\) | |
| 7056.bq3 | 7056w2 | \([0, 0, 0, -111279, -14224210]\) | \(6940769488/35721\) | \(784294811709696\) | \([2, 2]\) | \(36864\) | \(1.7039\) | |
| 7056.bq4 | 7056w1 | \([0, 0, 0, -3234, -459277]\) | \(-2725888/64827\) | \(-88959365217072\) | \([2]\) | \(18432\) | \(1.3573\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7056.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 7056.bq do not have complex multiplication.Modular form 7056.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
