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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 18720bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18720.bg3 | 18720bq1 | \([0, 0, 0, -14414817, 21063537376]\) | \(7099759044484031233216/577161945398025\) | \(26928067724490254400\) | \([2, 2]\) | \(860160\) | \(2.7734\) | \(\Gamma_0(N)\)-optimal |
| 18720.bg2 | 18720bq2 | \([0, 0, 0, -15403467, 18008806606]\) | \(1082883335268084577352/251301565117746585\) | \(93797806577068677358080\) | \([2]\) | \(1720320\) | \(3.1200\) | |
| 18720.bg1 | 18720bq3 | \([0, 0, 0, -230632572, 1348121630464]\) | \(454357982636417669333824/3003024375\) | \(8966982735360000\) | \([4]\) | \(1720320\) | \(3.1200\) | |
| 18720.bg4 | 18720bq4 | \([0, 0, 0, -13430667, 24063029746]\) | \(-717825640026599866952/254764560814329735\) | \(-95090362794826944929280\) | \([2]\) | \(1720320\) | \(3.1200\) |
Rank
sage: E.rank()
The elliptic curves in class 18720bq have rank \(1\).
Complex multiplication
The elliptic curves in class 18720bq do not have complex multiplication.Modular form 18720.2.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.
