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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 31790.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
31790.q1 | 31790o2 | \([1, 0, 0, -1716666, -865861870]\) | \(-23178622194826561/1610510\) | \(-38873796250190\) | \([]\) | \(440000\) | \(2.0617\) | |
31790.q2 | 31790o1 | \([1, 0, 0, 2884, -240400]\) | \(109902239/1100000\) | \(-26551325900000\) | \([]\) | \(88000\) | \(1.2570\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 31790.q have rank \(0\).
Complex multiplication
The elliptic curves in class 31790.q do not have complex multiplication.Modular form 31790.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.