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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 36225bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36225.l4 | 36225bk1 | \([1, -1, 1, -51980, -1185978]\) | \(1363569097969/734582625\) | \(8367355212890625\) | \([4]\) | \(202752\) | \(1.7464\) | \(\Gamma_0(N)\)-optimal |
| 36225.l2 | 36225bk2 | \([1, -1, 1, -647105, -199957728]\) | \(2630872462131649/3645140625\) | \(41520429931640625\) | \([2, 2]\) | \(405504\) | \(2.0929\) | |
| 36225.l3 | 36225bk3 | \([1, -1, 1, -465980, -314428728]\) | \(-982374577874929/3183837890625\) | \(-36265903472900390625\) | \([2]\) | \(811008\) | \(2.4395\) | |
| 36225.l1 | 36225bk4 | \([1, -1, 1, -10350230, -12814020228]\) | \(10765299591712341649/20708625\) | \(235884181640625\) | \([2]\) | \(811008\) | \(2.4395\) |
Rank
sage: E.rank()
The elliptic curves in class 36225bk have rank \(1\).
Complex multiplication
The elliptic curves in class 36225bk do not have complex multiplication.Modular form 36225.2.a.bk
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
