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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 28322.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28322.bb1 | 28322t4 | \([1, -1, 1, -7486744, 7883202345]\) | \(16342588257633/8185058\) | \(23243607306604591298\) | \([2]\) | \(884736\) | \(2.6687\) | |
| 28322.bb2 | 28322t2 | \([1, -1, 1, -547854, 78338873]\) | \(6403769793/2775556\) | \(7881915280440311236\) | \([2, 2]\) | \(442368\) | \(2.3221\) | |
| 28322.bb3 | 28322t1 | \([1, -1, 1, -264634, -51489175]\) | \(721734273/13328\) | \(37848332679185168\) | \([2]\) | \(221184\) | \(1.9755\) | \(\Gamma_0(N)\)-optimal |
| 28322.bb4 | 28322t3 | \([1, -1, 1, 1859516, 579071833]\) | \(250404380127/196003234\) | \(-556602311421681978754\) | \([2]\) | \(884736\) | \(2.6687\) |
Rank
sage: E.rank()
The elliptic curves in class 28322.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 28322.bb do not have complex multiplication.Modular form 28322.2.a.bb
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.
