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Properties

Label 19110f
Number of curves $2$
Conductor $19110$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 19110f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.k1 19110f1 \([1, 1, 0, -6052, -189986]\) \(-86806489/3510\) \(-991488123990\) \([]\) \(36288\) \(1.0698\) \(\Gamma_0(N)\)-optimal
19110.k2 19110f2 \([1, 1, 0, 29963, -557339]\) \(10531168151/6591000\) \(-1861794366159000\) \([]\) \(108864\) \(1.6191\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19110f have rank \(1\).

Complex multiplication

The elliptic curves in class 19110f do not have complex multiplication.

Modular form 19110.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - q^{12} - q^{13} - q^{15} + q^{16} + 3 q^{17} - q^{18} + q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.