Properties

Label 190440.n
Number of curves $4$
Conductor $190440$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 190440.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190440.n1 190440bk3 \([0, 0, 0, -5029203, 4271906702]\) \(63649751618/1164375\) \(257345968409475840000\) \([2]\) \(6488064\) \(2.7113\)  
190440.n2 190440bk2 \([0, 0, 0, -649083, -100329082]\) \(273671716/119025\) \(13153238385373209600\) \([2, 2]\) \(3244032\) \(2.3647\)  
190440.n3 190440bk1 \([0, 0, 0, -553863, -158584678]\) \(680136784/345\) \(9531332163313920\) \([2]\) \(1622016\) \(2.0181\) \(\Gamma_0(N)\)-optimal
190440.n4 190440bk4 \([0, 0, 0, 2207517, -744206722]\) \(5382838942/4197615\) \(-927741747448323717120\) \([2]\) \(6488064\) \(2.7113\)  

Rank

sage: E.rank()
 

The elliptic curves in class 190440.n have rank \(1\).

Complex multiplication

The elliptic curves in class 190440.n do not have complex multiplication.

Modular form 190440.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{11} + 2 q^{13} + 2 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.