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SageMath
sage: E = EllipticCurve("100.a1")
sage: E.isogeny_class()
Elliptic curves in class 100a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
100.a3 | 100a1 | [0, -1, 0, -33, 62] | [2] | 12 | \(\Gamma_0(N)\)-optimal |
100.a4 | 100a2 | [0, -1, 0, 92, 312] | [2] | 24 | |
100.a1 | 100a3 | [0, -1, 0, -1033, -12438] | [2] | 36 | |
100.a2 | 100a4 | [0, -1, 0, -908, -15688] | [2] | 72 |
Rank
sage: E.rank()
The elliptic curves in class 100a have rank \(0\).
Modular form 100.2.a.a
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.