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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 72128.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72128.s1 | 72128cf2 | \([0, 1, 0, -73761, -3365153]\) | \(5756278756/2705927\) | \(20863359754108928\) | \([2]\) | \(737280\) | \(1.8257\) | |
72128.s2 | 72128cf1 | \([0, 1, 0, 16399, -389873]\) | \(253012016/181447\) | \(-349750199959552\) | \([2]\) | \(368640\) | \(1.4791\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72128.s have rank \(0\).
Complex multiplication
The elliptic curves in class 72128.s do not have complex multiplication.Modular form 72128.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.