Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 19404r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19404.y2 | 19404r1 | \([0, 0, 0, 1176, -8575]\) | \(131072/99\) | \(-135853535664\) | \([2]\) | \(17280\) | \(0.82439\) | \(\Gamma_0(N)\)-optimal |
19404.y1 | 19404r2 | \([0, 0, 0, -5439, -73402]\) | \(810448/363\) | \(7970074092288\) | \([2]\) | \(34560\) | \(1.1710\) |
Rank
sage: E.rank()
The elliptic curves in class 19404r have rank \(0\).
Complex multiplication
The elliptic curves in class 19404r do not have complex multiplication.Modular form 19404.2.a.r
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.