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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 474075bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 474075.bg2 | 474075bg1 | \([1, -1, 1, -861357755, -9728893083878]\) | \(1953326569433829507/262451171875\) | \(9496161125278472900390625\) | \([2]\) | \(185794560\) | \(3.8116\) | \(\Gamma_0(N)\)-optimal |
| 474075.bg1 | 474075bg2 | \([1, -1, 1, -13781279630, -622701666521378]\) | \(8000051600110940079507/144453125\) | \(5226687083353271484375\) | \([2]\) | \(371589120\) | \(4.1582\) |
Rank
sage: E.rank()
The elliptic curves in class 474075bg have rank \(1\).
Complex multiplication
The elliptic curves in class 474075bg do not have complex multiplication.Modular form 474075.2.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.
