Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 10143.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10143.p1 | 10143r3 | \([1, -1, 0, -54546, 4915889]\) | \(209267191953/55223\) | \(4736262499983\) | \([2]\) | \(30720\) | \(1.4166\) | |
| 10143.p2 | 10143r2 | \([1, -1, 0, -3831, 57392]\) | \(72511713/25921\) | \(2223143622441\) | \([2, 2]\) | \(15360\) | \(1.0701\) | |
| 10143.p3 | 10143r1 | \([1, -1, 0, -1626, -24193]\) | \(5545233/161\) | \(13808345481\) | \([2]\) | \(7680\) | \(0.72348\) | \(\Gamma_0(N)\)-optimal |
| 10143.p4 | 10143r4 | \([1, -1, 0, 11604, 393875]\) | \(2014698447/1958887\) | \(-168006139467327\) | \([2]\) | \(30720\) | \(1.4166\) |
Rank
sage: E.rank()
The elliptic curves in class 10143.p have rank \(0\).
Complex multiplication
The elliptic curves in class 10143.p do not have complex multiplication.Modular form 10143.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
