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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 44880cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44880.cm2 | 44880cv1 | \([0, 1, 0, -185960, 30649908]\) | \(173629978755828841/1000026931200\) | \(4096110310195200\) | \([2]\) | \(337920\) | \(1.8369\) | \(\Gamma_0(N)\)-optimal |
44880.cm1 | 44880cv2 | \([0, 1, 0, -2971240, 1970318900]\) | \(708234550511150304361/23696640000\) | \(97061437440000\) | \([2]\) | \(675840\) | \(2.1834\) |
Rank
sage: E.rank()
The elliptic curves in class 44880cv have rank \(1\).
Complex multiplication
The elliptic curves in class 44880cv do not have complex multiplication.Modular form 44880.2.a.cv
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.