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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 44880cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44880.cf2 | 44880cq1 | \([0, 1, 0, -364616, 464399220]\) | \(-1308796492121439049/22000592486400000\) | \(-90114426824294400000\) | \([2]\) | \(1198080\) | \(2.5102\) | \(\Gamma_0(N)\)-optimal |
44880.cf1 | 44880cq2 | \([0, 1, 0, -11505736, 14961224564]\) | \(41125104693338423360329/179205840000000000\) | \(734027120640000000000\) | \([2]\) | \(2396160\) | \(2.8568\) |
Rank
sage: E.rank()
The elliptic curves in class 44880cq have rank \(1\).
Complex multiplication
The elliptic curves in class 44880cq do not have complex multiplication.Modular form 44880.2.a.cq
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 Cremona 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 Cremona labels.