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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 371800.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
371800.bb1 | 371800bb1 | \([0, 0, 0, -160550, -23892375]\) | \(379275264/15125\) | \(18251371531250000\) | \([2]\) | \(2709504\) | \(1.8868\) | \(\Gamma_0(N)\)-optimal |
371800.bb2 | 371800bb2 | \([0, 0, 0, 71825, -87330750]\) | \(2122416/171875\) | \(-3318431187500000000\) | \([2]\) | \(5419008\) | \(2.2333\) |
Rank
sage: E.rank()
The elliptic curves in class 371800.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 371800.bb do not have complex multiplication.Modular form 371800.2.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.