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Properties

Label 19110db
Number of curves $2$
Conductor $19110$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("db1")
 
E.isogeny_class()
 

Elliptic curves in class 19110db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.cz2 19110db1 \([1, 0, 0, -6910, -223588]\) \(-744673162316209/7529822040\) \(-368961279960\) \([]\) \(28224\) \(1.0381\) \(\Gamma_0(N)\)-optimal
19110.cz1 19110db2 \([1, 0, 0, -38760, 23169600]\) \(-131425499875625809/4658135040000000\) \(-228248616960000000\) \([7]\) \(197568\) \(2.0110\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 19110.2.a.db

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} - q^{13} + q^{15} + q^{16} - 3 q^{17} + q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.