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SageMath
sage: E = EllipticCurve("b1")
sage: E.isogeny_class()
Elliptic curves in class 144.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
144.b1 | 144b5 | [0, 0, 0, -3459, -78302] | [2] | 64 | |
144.b2 | 144b4 | [0, 0, 0, -579, 5362] | [4] | 32 | |
144.b3 | 144b3 | [0, 0, 0, -219, -1190] | [2, 2] | 32 | |
144.b4 | 144b2 | [0, 0, 0, -39, 70] | [2, 2] | 16 | |
144.b5 | 144b1 | [0, 0, 0, 6, 7] | [2] | 8 | \(\Gamma_0(N)\)-optimal |
144.b6 | 144b6 | [0, 0, 0, 141, -4718] | [2] | 64 |
Rank
sage: E.rank()
The elliptic curves in class 144.b have rank \(0\).
Complex multiplication
The elliptic curves in class 144.b do not have complex multiplication.Modular form 144.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.