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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 301530.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 301530.bq1 | 301530bq4 | \([1, 1, 1, -260521931, -1618615418011]\) | \(13209596798923694545921/92340\) | \(13669633990260\) | \([2]\) | \(43253760\) | \(3.0552\) | |
| 301530.bq2 | 301530bq3 | \([1, 1, 1, -16483651, -24639550027]\) | \(3345930611358906241/165622259047500\) | \(24518038356284955727500\) | \([2]\) | \(43253760\) | \(3.0552\) | |
| 301530.bq3 | 301530bq2 | \([1, 1, 1, -16282631, -25295920531]\) | \(3225005357698077121/8526675600\) | \(1262254002660608400\) | \([2, 2]\) | \(21626880\) | \(2.7087\) | |
| 301530.bq4 | 301530bq1 | \([1, 1, 1, -1005111, -405784947]\) | \(-758575480593601/40535043840\) | \(-6000641250508373760\) | \([2]\) | \(10813440\) | \(2.3621\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 301530.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 301530.bq do not have complex multiplication.Modular form 301530.2.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.
