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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 141570.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141570.q1 | 141570dw4 | \([1, -1, 0, -61160985, -184087266269]\) | \(19591310611933007401/154169730\) | \(199105268084378370\) | \([2]\) | \(9830400\) | \(2.9104\) | |
| 141570.q2 | 141570dw3 | \([1, -1, 0, -5382405, -311115425]\) | \(13352704496588521/7694601378750\) | \(9937331214878862258750\) | \([2]\) | \(9830400\) | \(2.9104\) | |
| 141570.q3 | 141570dw2 | \([1, -1, 0, -3825135, -2871578759]\) | \(4792702134385801/13416588900\) | \(17327094817590944100\) | \([2, 2]\) | \(4915200\) | \(2.5639\) | |
| 141570.q4 | 141570dw1 | \([1, -1, 0, -144315, -80781035]\) | \(-257380823881/2035828080\) | \(-2629206755710769520\) | \([2]\) | \(2457600\) | \(2.2173\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141570.q have rank \(0\).
Complex multiplication
The elliptic curves in class 141570.q do not have complex multiplication.Modular form 141570.2.a.q
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.
