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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 158.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158.b1 | 158d2 | \([1, 0, 1, -5217, -145452]\) | \(15698803397448457/20709376\) | \(20709376\) | \([]\) | \(120\) | \(0.67986\) | |
158.b2 | 158d1 | \([1, 0, 1, -82, -92]\) | \(59914169497/31554496\) | \(31554496\) | \([3]\) | \(40\) | \(0.13055\) | \(\Gamma_0(N)\)-optimal |
158.b3 | 158d3 | \([1, 0, 1, -47, 118]\) | \(11134383337/316\) | \(316\) | \([3]\) | \(120\) | \(-0.41875\) |
Rank
sage: E.rank()
The elliptic curves in class 158.b have rank \(0\).
Complex multiplication
The elliptic curves in class 158.b do not have complex multiplication.Modular form 158.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.