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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 150590.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
150590.c1 | 150590o2 | \([1, 1, 0, -8131888, -8928943978]\) | \(-23178622194826561/1610510\) | \(-4132128038958590\) | \([]\) | \(5166000\) | \(2.4505\) | |
150590.c2 | 150590o1 | \([1, 1, 0, 13662, -2475308]\) | \(109902239/1100000\) | \(-2822299049900000\) | \([]\) | \(1033200\) | \(1.6458\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 150590.c have rank \(0\).
Complex multiplication
The elliptic curves in class 150590.c do not have complex multiplication.Modular form 150590.2.a.c
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.