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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 49686bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49686.bj2 | 49686bg1 | \([1, 0, 1, -173, -2026]\) | \(-2401/6\) | \(-1419081846\) | \([]\) | \(28224\) | \(0.44400\) | \(\Gamma_0(N)\)-optimal |
49686.bj1 | 49686bg2 | \([1, 0, 1, -23833, 1467260]\) | \(-6329617441/279936\) | \(-66208682606976\) | \([]\) | \(197568\) | \(1.4170\) |
Rank
sage: E.rank()
The elliptic curves in class 49686bg have rank \(1\).
Complex multiplication
The elliptic curves in class 49686bg do not have complex multiplication.Modular form 49686.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.