Show commands:
SageMath
E = EllipticCurve("hs1")
E.isogeny_class()
Elliptic curves in class 179520hs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179520.d2 | 179520hs1 | \([0, -1, 0, 102079, 12710721]\) | \(448733772344879/527357952000\) | \(-138243722969088000\) | \([2]\) | \(2064384\) | \(1.9753\) | \(\Gamma_0(N)\)-optimal |
179520.d1 | 179520hs2 | \([0, -1, 0, -594241, 121475905]\) | \(88526309511756241/26991954000000\) | \(7075778789376000000\) | \([2]\) | \(4128768\) | \(2.3218\) |
Rank
sage: E.rank()
The elliptic curves in class 179520hs have rank \(1\).
Complex multiplication
The elliptic curves in class 179520hs do not have complex multiplication.Modular form 179520.2.a.hs
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.