Properties

Label 19350y
Number of curves $2$
Conductor $19350$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19350y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19350.bf2 19350y1 \([1, -1, 0, -8442, -198284]\) \(5841725401/1857600\) \(21159225000000\) \([2]\) \(55296\) \(1.2608\) \(\Gamma_0(N)\)-optimal
19350.bf1 19350y2 \([1, -1, 0, -53442, 4616716]\) \(1481933914201/53916840\) \(614146505625000\) \([2]\) \(110592\) \(1.6073\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19350y have rank \(1\).

Complex multiplication

The elliptic curves in class 19350y do not have complex multiplication.

Modular form 19350.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2q^{7} - q^{8} + 2q^{11} + 2q^{13} - 2q^{14} + q^{16} - 4q^{17} - 6q^{19} + O(q^{20})\)  Toggle raw display

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.