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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 43890o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43890.p4 | 43890o1 | \([1, 1, 0, 8663, 123781]\) | \(71886993644327399/47839869665280\) | \(-47839869665280\) | \([2]\) | \(143360\) | \(1.3137\) | \(\Gamma_0(N)\)-optimal |
| 43890.p3 | 43890o2 | \([1, 1, 0, -37417, 980869]\) | \(5793603095825296921/2923833093350400\) | \(2923833093350400\) | \([2, 2]\) | \(286720\) | \(1.6602\) | |
| 43890.p2 | 43890o3 | \([1, 1, 0, -327817, -71677211]\) | \(3896011200849402602521/43634030575507680\) | \(43634030575507680\) | \([2]\) | \(573440\) | \(2.0068\) | |
| 43890.p1 | 43890o4 | \([1, 1, 0, -484297, 129414181]\) | \(12562048033845592406041/11974087092660000\) | \(11974087092660000\) | \([2]\) | \(573440\) | \(2.0068\) |
Rank
sage: E.rank()
The elliptic curves in class 43890o have rank \(1\).
Complex multiplication
The elliptic curves in class 43890o do not have complex multiplication.Modular form 43890.2.a.o
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.
