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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 32448bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32448.da3 | 32448bg1 | \([0, 1, 0, -732, 7242]\) | \(140608/3\) | \(926747328\) | \([2]\) | \(18432\) | \(0.50968\) | \(\Gamma_0(N)\)-optimal |
| 32448.da2 | 32448bg2 | \([0, 1, 0, -1577, -13545]\) | \(21952/9\) | \(177935486976\) | \([2, 2]\) | \(36864\) | \(0.85625\) | |
| 32448.da4 | 32448bg3 | \([0, 1, 0, 5183, -93313]\) | \(97336/81\) | \(-12811355062272\) | \([2]\) | \(73728\) | \(1.2028\) | |
| 32448.da1 | 32448bg4 | \([0, 1, 0, -21857, -1250625]\) | \(7301384/3\) | \(474494631936\) | \([2]\) | \(73728\) | \(1.2028\) |
Rank
sage: E.rank()
The elliptic curves in class 32448bg have rank \(0\).
Complex multiplication
The elliptic curves in class 32448bg do not have complex multiplication.Modular form 32448.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
