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Properties

Label 19110.l
Number of curves $2$
Conductor $19110$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 19110.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.l1 19110i1 \([1, 1, 0, -137, 561]\) \(838561807/3900\) \(1337700\) \([2]\) \(5120\) \(0.025744\) \(\Gamma_0(N)\)-optimal
19110.l2 19110i2 \([1, 1, 0, -67, 1219]\) \(-99252847/1901250\) \(-652128750\) \([2]\) \(10240\) \(0.37232\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 19110.2.a.l

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