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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 48510.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48510.bq1 | 48510bv4 | \([1, -1, 0, -21732489, -38989871915]\) | \(13235378341603461121/9240\) | \(792478958040\) | \([2]\) | \(1179648\) | \(2.4962\) | |
| 48510.bq2 | 48510bv2 | \([1, -1, 0, -1358289, -608953955]\) | \(3231355012744321/85377600\) | \(7322505572289600\) | \([2, 2]\) | \(589824\) | \(2.1497\) | |
| 48510.bq3 | 48510bv3 | \([1, -1, 0, -1305369, -658624667]\) | \(-2868190647517441/527295615000\) | \(-45224099518859415000\) | \([2]\) | \(1179648\) | \(2.4962\) | |
| 48510.bq4 | 48510bv1 | \([1, -1, 0, -88209, -8714147]\) | \(885012508801/127733760\) | \(10955229115944960\) | \([2]\) | \(294912\) | \(1.8031\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 48510.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 48510.bq do not have complex multiplication.Modular form 48510.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
