Show commands:
SageMath
E = EllipticCurve("hi1")
E.isogeny_class()
Elliptic curves in class 203280.hi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.hi1 | 203280n3 | \([0, 1, 0, -40080080, -27683936172]\) | \(981281029968144361/522287841796875\) | \(3789884503251000000000000\) | \([4]\) | \(35389440\) | \(3.4076\) | |
| 203280.hi2 | 203280n2 | \([0, 1, 0, -31455200, -67837927500]\) | \(474334834335054841/607815140625\) | \(4410497426803776000000\) | \([2, 2]\) | \(17694720\) | \(3.0610\) | |
| 203280.hi3 | 203280n1 | \([0, 1, 0, -31445520, -67881801132]\) | \(473897054735271721/779625\) | \(5657203689984000\) | \([2]\) | \(8847360\) | \(2.7144\) | \(\Gamma_0(N)\)-optimal |
| 203280.hi4 | 203280n4 | \([0, 1, 0, -22985200, -105183851500]\) | \(-185077034913624841/551466161890875\) | \(-4001611551643895422464000\) | \([2]\) | \(35389440\) | \(3.4076\) |
Rank
sage: E.rank()
The elliptic curves in class 203280.hi have rank \(0\).
Complex multiplication
The elliptic curves in class 203280.hi do not have complex multiplication.Modular form 203280.2.a.hi
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.
