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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 134064.dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134064.dg1 | 134064bo3 | \([0, 0, 0, -3020115, 2020132114]\) | \(8671983378625/82308\) | \(28914638386249728\) | \([2]\) | \(1990656\) | \(2.3209\) | |
| 134064.dg2 | 134064bo4 | \([0, 0, 0, -2949555, 2119014898]\) | \(-8078253774625/846825858\) | \(-297488257036930326528\) | \([2]\) | \(3981312\) | \(2.6675\) | |
| 134064.dg3 | 134064bo1 | \([0, 0, 0, -56595, -395822]\) | \(57066625/32832\) | \(11533816974016512\) | \([2]\) | \(663552\) | \(1.7716\) | \(\Gamma_0(N)\)-optimal |
| 134064.dg4 | 134064bo2 | \([0, 0, 0, 225645, -3161774]\) | \(3616805375/2105352\) | \(-739606013458808832\) | \([2]\) | \(1327104\) | \(2.1182\) |
Rank
sage: E.rank()
The elliptic curves in class 134064.dg have rank \(1\).
Complex multiplication
The elliptic curves in class 134064.dg do not have complex multiplication.Modular form 134064.2.a.dg
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
