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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 113568.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 113568.bb1 | 113568b4 | \([0, -1, 0, -37912, 2853928]\) | \(2438569736/21\) | \(51897850368\) | \([2]\) | \(245760\) | \(1.2238\) | |
| 113568.bb2 | 113568b3 | \([0, -1, 0, -8337, -241983]\) | \(3241792/567\) | \(11209935679488\) | \([2]\) | \(245760\) | \(1.2238\) | |
| 113568.bb3 | 113568b1 | \([0, -1, 0, -2422, 43120]\) | \(5088448/441\) | \(136231857216\) | \([2, 2]\) | \(122880\) | \(0.87727\) | \(\Gamma_0(N)\)-optimal |
| 113568.bb4 | 113568b2 | \([0, -1, 0, 2648, 195220]\) | \(830584/7203\) | \(-17800962676224\) | \([2]\) | \(245760\) | \(1.2238\) |
Rank
sage: E.rank()
The elliptic curves in class 113568.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 113568.bb do not have complex multiplication.Modular form 113568.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
