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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1008.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1008.b1 | 1008e4 | \([0, 0, 0, -36291, 2661010]\) | \(7080974546692/189\) | \(141087744\) | \([4]\) | \(1536\) | \(1.0775\) | |
| 1008.b2 | 1008e3 | \([0, 0, 0, -3531, -9686]\) | \(6522128932/3720087\) | \(2777030065152\) | \([2]\) | \(1536\) | \(1.0775\) | |
| 1008.b3 | 1008e2 | \([0, 0, 0, -2271, 41470]\) | \(6940769488/35721\) | \(6666395904\) | \([2, 2]\) | \(768\) | \(0.73092\) | |
| 1008.b4 | 1008e1 | \([0, 0, 0, -66, 1339]\) | \(-2725888/64827\) | \(-756142128\) | \([2]\) | \(384\) | \(0.38435\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1008.b have rank \(0\).
Complex multiplication
The elliptic curves in class 1008.b do not have complex multiplication.Modular form 1008.2.a.b
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.
