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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 3920.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3920.s1 | 3920d3 | \([0, 0, 0, -5243, -146118]\) | \(132304644/5\) | \(602362880\) | \([2]\) | \(2304\) | \(0.77074\) | |
3920.s2 | 3920d2 | \([0, 0, 0, -343, -2058]\) | \(148176/25\) | \(752953600\) | \([2, 2]\) | \(1152\) | \(0.42417\) | |
3920.s3 | 3920d1 | \([0, 0, 0, -98, 343]\) | \(55296/5\) | \(9411920\) | \([2]\) | \(576\) | \(0.077594\) | \(\Gamma_0(N)\)-optimal |
3920.s4 | 3920d4 | \([0, 0, 0, 637, -11662]\) | \(237276/625\) | \(-75295360000\) | \([2]\) | \(2304\) | \(0.77074\) |
Rank
sage: E.rank()
The elliptic curves in class 3920.s have rank \(0\).
Complex multiplication
The elliptic curves in class 3920.s do not have complex multiplication.Modular form 3920.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.