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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 151008bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
151008.bl2 | 151008bg1 | \([0, 1, 0, -2218, 39092]\) | \(10648000/117\) | \(13265448768\) | \([2]\) | \(92160\) | \(0.75706\) | \(\Gamma_0(N)\)-optimal |
151008.bl1 | 151008bg2 | \([0, 1, 0, -4033, -36049]\) | \(1000000/507\) | \(3678951124992\) | \([2]\) | \(184320\) | \(1.1036\) |
Rank
sage: E.rank()
The elliptic curves in class 151008bg have rank \(1\).
Complex multiplication
The elliptic curves in class 151008bg do not have complex multiplication.Modular form 151008.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.