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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 317900.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
317900.bb1 | 317900bb1 | \([0, -1, 0, -2139765633, -38061362887738]\) | \(179551401487197159424/193592864403125\) | \(1168215280609518375781250000\) | \([2]\) | \(205701120\) | \(4.1096\) | \(\Gamma_0(N)\)-optimal |
317900.bb2 | 317900bb2 | \([0, -1, 0, -1610859508, -57342106768488]\) | \(-4787879231470062544/11941708603515625\) | \(-1152975261581008164062500000000\) | \([2]\) | \(411402240\) | \(4.4562\) |
Rank
sage: E.rank()
The elliptic curves in class 317900.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 317900.bb do not have complex multiplication.Modular form 317900.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.