Properties

Label 190740.k
Number of curves $4$
Conductor $190740$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 190740.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190740.k1 190740u4 \([0, -1, 0, -72248940, -236347539288]\) \(6749703004355978704/5671875\) \(35047750188000000\) \([2]\) \(8957952\) \(2.9102\)  
190740.k2 190740u3 \([0, -1, 0, -4514565, -3693508038]\) \(-26348629355659264/24169921875\) \(-9334450511718750000\) \([2]\) \(4478976\) \(2.5636\)  
190740.k3 190740u2 \([0, -1, 0, -912180, -308467800]\) \(13584145739344/1195803675\) \(7389131191236115200\) \([2]\) \(2985984\) \(2.3609\)  
190740.k4 190740u1 \([0, -1, 0, 63195, -22487850]\) \(72268906496/606436875\) \(-234206590631310000\) \([2]\) \(1492992\) \(2.0143\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 190740.k have rank \(1\).

Complex multiplication

The elliptic curves in class 190740.k do not have complex multiplication.

Modular form 190740.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 2q^{7} + q^{9} - q^{11} + 2q^{13} - q^{15} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.