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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 7488.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7488.bf1 | 7488k4 | \([0, 0, 0, -26940, 1579952]\) | \(181037698000/14480427\) | \(172953293340672\) | \([2]\) | \(18432\) | \(1.4753\) | |
| 7488.bf2 | 7488k3 | \([0, 0, 0, -26400, 1651016]\) | \(2725888000000/19773\) | \(14760465408\) | \([2]\) | \(9216\) | \(1.1288\) | |
| 7488.bf3 | 7488k2 | \([0, 0, 0, -5340, -149776]\) | \(1409938000/4563\) | \(54500179968\) | \([2]\) | \(6144\) | \(0.92603\) | |
| 7488.bf4 | 7488k1 | \([0, 0, 0, -480, -88]\) | \(16384000/9477\) | \(7074542592\) | \([2]\) | \(3072\) | \(0.57946\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7488.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 7488.bf do not have complex multiplication.Modular form 7488.2.a.bf
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
