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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 147294bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
147294.cp2 | 147294bg1 | \([1, -1, 1, -1994, -141879]\) | \(-10218313/96192\) | \(-8250014711232\) | \([2]\) | \(331776\) | \(1.1608\) | \(\Gamma_0(N)\)-optimal |
147294.cp1 | 147294bg2 | \([1, -1, 1, -54914, -4925847]\) | \(213525509833/669336\) | \(57406352365656\) | \([2]\) | \(663552\) | \(1.5074\) |
Rank
sage: E.rank()
The elliptic curves in class 147294bg have rank \(1\).
Complex multiplication
The elliptic curves in class 147294bg do not have complex multiplication.Modular form 147294.2.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.