Properties

Label 19110.di
Number of curves $2$
Conductor $19110$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("di1")
 
E.isogeny_class()
 

Elliptic curves in class 19110.di

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.di1 19110dh2 \([1, 0, 0, -4408755, -3563418573]\) \(27629784261491295969847/311852531250\) \(106965418218750\) \([2]\) \(506880\) \(2.2601\)  
19110.di2 19110dh1 \([1, 0, 0, -275325, -55789875]\) \(-6729249553378150807/22664098606500\) \(-7773785822029500\) \([2]\) \(253440\) \(1.9135\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 19110.di have rank \(0\).

Complex multiplication

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

Modular form 19110.2.a.di

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