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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 600.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
600.a1 | 600f3 | \([0, -1, 0, -5408, -151188]\) | \(546718898/405\) | \(12960000000\) | \([2]\) | \(768\) | \(0.87412\) | |
600.a2 | 600f4 | \([0, -1, 0, -3408, 76812]\) | \(136835858/1875\) | \(60000000000\) | \([2]\) | \(768\) | \(0.87412\) | |
600.a3 | 600f2 | \([0, -1, 0, -408, -1188]\) | \(470596/225\) | \(3600000000\) | \([2, 2]\) | \(384\) | \(0.52755\) | |
600.a4 | 600f1 | \([0, -1, 0, 92, -188]\) | \(21296/15\) | \(-60000000\) | \([4]\) | \(192\) | \(0.18097\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 600.a have rank \(0\).
Complex multiplication
The elliptic curves in class 600.a do not have complex multiplication.Modular form 600.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.