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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 4800.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4800.s1 | 4800a3 | \([0, -1, 0, -16033, -776063]\) | \(890277128/15\) | \(7680000000\) | \([2]\) | \(6144\) | \(1.0271\) | |
4800.s2 | 4800a4 | \([0, -1, 0, -4033, 87937]\) | \(14172488/1875\) | \(960000000000\) | \([2]\) | \(6144\) | \(1.0271\) | |
4800.s3 | 4800a2 | \([0, -1, 0, -1033, -11063]\) | \(1906624/225\) | \(14400000000\) | \([2, 2]\) | \(3072\) | \(0.68052\) | |
4800.s4 | 4800a1 | \([0, -1, 0, 92, -938]\) | \(85184/405\) | \(-405000000\) | \([2]\) | \(1536\) | \(0.33395\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4800.s have rank \(1\).
Complex multiplication
The elliptic curves in class 4800.s do not have complex multiplication.Modular form 4800.2.a.s
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.