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SageMath
sage: E = EllipticCurve("900.b1")
sage: E.isogeny_class()
Elliptic curves in class 900e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
900.b3 | 900e1 | [0, 0, 0, -300, -1375] | [2] | 288 | \(\Gamma_0(N)\)-optimal |
900.b4 | 900e2 | [0, 0, 0, 825, -9250] | [2] | 576 | |
900.b1 | 900e3 | [0, 0, 0, -9300, 345125] | [2] | 864 | |
900.b2 | 900e4 | [0, 0, 0, -8175, 431750] | [2] | 1728 |
Rank
sage: E.rank()
The elliptic curves in class 900e have rank \(1\).
Modular form 900.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.