Show commands:
SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 182070du
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 182070.be2 | 182070du1 | \([1, -1, 0, -30399, 2045113]\) | \(4767078987/6860\) | \(4470760530180\) | \([2]\) | \(497664\) | \(1.3298\) | \(\Gamma_0(N)\)-optimal |
| 182070.be3 | 182070du2 | \([1, -1, 0, -21729, 3229435]\) | \(-1740992427/5882450\) | \(-3833677154629350\) | \([2]\) | \(995328\) | \(1.6764\) | |
| 182070.be1 | 182070du3 | \([1, -1, 0, -121434, -14242060]\) | \(416832723/56000\) | \(26605587155112000\) | \([2]\) | \(1492992\) | \(1.8791\) | |
| 182070.be4 | 182070du4 | \([1, -1, 0, 190686, -75604852]\) | \(1613964717/6125000\) | \(-2909986095090375000\) | \([2]\) | \(2985984\) | \(2.2257\) |
Rank
sage: E.rank()
The elliptic curves in class 182070du have rank \(0\).
Complex multiplication
The elliptic curves in class 182070du do not have complex multiplication.Modular form 182070.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
