Properties

Label 194040.bq
Number of curves $4$
Conductor $194040$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bq1")
 
E.isogeny_class()
 

Elliptic curves in class 194040.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
194040.bq1 194040z4 \([0, 0, 0, -7185961083, -207660178566218]\) \(233632133015204766393938/29145526885986328125\) \(5119383112729101562500000000000\) \([2]\) \(377487360\) \(4.6222\)  
194040.bq2 194040z2 \([0, 0, 0, -1794947763, 25909786333438]\) \(7282213870869695463556/912102595400390625\) \(80104961599000520490000000000\) \([2, 2]\) \(188743680\) \(4.2756\)  
194040.bq3 194040z1 \([0, 0, 0, -1737079743, 27865736983042]\) \(26401417552259125806544/507547744790625\) \(11143782731005405034400000\) \([2]\) \(94371840\) \(3.9291\) \(\Gamma_0(N)\)-optimal
194040.bq4 194040z3 \([0, 0, 0, 2670177237, 134298909658438]\) \(11986661998777424518222/51295853620928503125\) \(-9010066203547324685040902400000\) \([2]\) \(377487360\) \(4.6222\)  

Rank

sage: E.rank()
 

The elliptic curves in class 194040.bq have rank \(1\).

Complex multiplication

The elliptic curves in class 194040.bq do not have complex multiplication.

Modular form 194040.2.a.bq

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{11} - 2 q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.