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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 137280du
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 137280.bq4 | 137280du1 | \([0, -1, 0, 4159, 132705]\) | \(30342134159/47190000\) | \(-12370575360000\) | \([2]\) | \(393216\) | \(1.1975\) | \(\Gamma_0(N)\)-optimal |
| 137280.bq3 | 137280du2 | \([0, -1, 0, -27841, 1367905]\) | \(9104453457841/2226896100\) | \(583767451238400\) | \([2, 2]\) | \(786432\) | \(1.5440\) | |
| 137280.bq1 | 137280du3 | \([0, -1, 0, -415041, 103046625]\) | \(30161840495801041/2799263610\) | \(733810159779840\) | \([2]\) | \(1572864\) | \(1.8906\) | |
| 137280.bq2 | 137280du4 | \([0, -1, 0, -152641, -21770015]\) | \(1500376464746641/83599963590\) | \(21915228855336960\) | \([2]\) | \(1572864\) | \(1.8906\) |
Rank
sage: E.rank()
The elliptic curves in class 137280du have rank \(0\).
Complex multiplication
The elliptic curves in class 137280du do not have complex multiplication.Modular form 137280.2.a.du
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.
