Show commands:
SageMath
E = EllipticCurve("gq1")
E.isogeny_class()
Elliptic curves in class 414050gq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414050.gq2 | 414050gq1 | \([1, 0, 0, 616762, 117687842]\) | \(17303/14\) | \(-20993416411390718750\) | \([]\) | \(9704448\) | \(2.3954\) | \(\Gamma_0(N)\)-optimal* |
414050.gq1 | 414050gq2 | \([1, 0, 0, -12839863, 17974629217]\) | \(-156116857/2744\) | \(-4114709616632580875000\) | \([]\) | \(29113344\) | \(2.9447\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414050gq have rank \(1\).
Complex multiplication
The elliptic curves in class 414050gq do not have complex multiplication.Modular form 414050.2.a.gq
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.