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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 18150bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18150.bb1 | 18150bg1 | \([1, 0, 1, -109266, -13921052]\) | \(-3257444411545/2737152\) | \(-121225793356800\) | \([]\) | \(144000\) | \(1.6301\) | \(\Gamma_0(N)\)-optimal |
18150.bb2 | 18150bg2 | \([1, 0, 1, 754674, 117194548]\) | \(2747555975/1932612\) | \(-33434961399726562500\) | \([]\) | \(720000\) | \(2.4348\) |
Rank
sage: E.rank()
The elliptic curves in class 18150bg have rank \(1\).
Complex multiplication
The elliptic curves in class 18150bg do not have complex multiplication.Modular form 18150.2.a.bg
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.