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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 148720.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 148720.bq1 | 148720bb4 | \([0, -1, 0, -1199956, 506336700]\) | \(154639330142416/33275\) | \(41116689785600\) | \([2]\) | \(1866240\) | \(1.9969\) | |
| 148720.bq2 | 148720bb3 | \([0, -1, 0, -75261, 7871876]\) | \(610462990336/8857805\) | \(684078926307920\) | \([2]\) | \(933120\) | \(1.6504\) | |
| 148720.bq3 | 148720bb2 | \([0, -1, 0, -16956, 485900]\) | \(436334416/171875\) | \(212379596000000\) | \([2]\) | \(622080\) | \(1.4476\) | |
| 148720.bq4 | 148720bb1 | \([0, -1, 0, -7661, -250264]\) | \(643956736/15125\) | \(1168087778000\) | \([2]\) | \(311040\) | \(1.1010\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 148720.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 148720.bq do not have complex multiplication.Modular form 148720.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
