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Properties

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

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 19110h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.h2 19110h1 \([1, 1, 0, -446597197, 2132451124189]\) \(244112114391139785383263/92579080750403420160\) \(3735899841023044708592517120\) \([2]\) \(12579840\) \(3.9901\) \(\Gamma_0(N)\)-optimal
19110.h1 19110h2 \([1, 1, 0, -6291097677, 192005076018141]\) \(682371118085879605963267423/216558834602980147200\) \(8738930103946661888910950400\) \([2]\) \(25159680\) \(4.3367\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 19110.2.a.h

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.