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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 253575.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 253575.ba1 | 253575ba3 | \([1, -1, 1, -507161255, 4396223260622]\) | \(10765299591712341649/20708625\) | \(27751538085837890625\) | \([2]\) | \(38928384\) | \(3.4125\) | |
| 253575.ba2 | 253575ba2 | \([1, -1, 1, -31708130, 68648916872]\) | \(2630872462131649/3645140625\) | \(4884837061027587890625\) | \([2, 2]\) | \(19464192\) | \(3.0659\) | |
| 253575.ba3 | 253575ba4 | \([1, -1, 1, -22833005, 107894719622]\) | \(-982374577874929/3183837890625\) | \(-4266647277683258056640625\) | \([2]\) | \(38928384\) | \(3.4125\) | |
| 253575.ba4 | 253575ba1 | \([1, -1, 1, -2547005, 411884372]\) | \(1363569097969/734582625\) | \(984410973441369140625\) | \([2]\) | \(9732096\) | \(2.7193\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 253575.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 253575.ba do not have complex multiplication.Modular form 253575.2.a.ba
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.
