Show commands:
SageMath
E = EllipticCurve("hw1")
E.isogeny_class()
Elliptic curves in class 152880hw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.h2 | 152880hw1 | \([0, -1, 0, -1020196, -376123040]\) | \(11367178023472/651619215\) | \(6731567543234177280\) | \([2]\) | \(3354624\) | \(2.3669\) | \(\Gamma_0(N)\)-optimal |
| 152880.h1 | 152880hw2 | \([0, -1, 0, -16091616, -24840051984]\) | \(11151682683009628/40040325\) | \(1654550056143129600\) | \([2]\) | \(6709248\) | \(2.7135\) |
Rank
sage: E.rank()
The elliptic curves in class 152880hw have rank \(0\).
Complex multiplication
The elliptic curves in class 152880hw do not have complex multiplication.Modular form 152880.2.a.hw
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
