Properties

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

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 19110g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.i2 19110g1 \([1, 1, 0, -1432, 34336]\) \(-6634840273369/6918968160\) \(-339029439840\) \([]\) \(25920\) \(0.90770\) \(\Gamma_0(N)\)-optimal
19110.i1 19110g2 \([1, 1, 0, -136567, 19368469]\) \(-5748703487739833929/1437696000\) \(-70447104000\) \([]\) \(77760\) \(1.4570\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 19110.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - q^{12} - q^{13} - q^{15} + q^{16} - 3 q^{17} - q^{18} + 7 q^{19} + O(q^{20})\) 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.