Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 116610q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116610.w2 | 116610q1 | \([1, 1, 0, -560407, 163211989]\) | \(-4032510095423809/57316147200\) | \(-276654095150284800\) | \([2]\) | \(4128768\) | \(2.1521\) | \(\Gamma_0(N)\)-optimal |
116610.w1 | 116610q2 | \([1, 1, 0, -8996887, 10383163861]\) | \(16685547865377876289/3300960000\) | \(15933103436640000\) | \([2]\) | \(8257536\) | \(2.4987\) |
Rank
sage: E.rank()
The elliptic curves in class 116610q have rank \(0\).
Complex multiplication
The elliptic curves in class 116610q do not have complex multiplication.Modular form 116610.2.a.q
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.