Properties

Label 227136q
Number of curves $4$
Conductor $227136$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 227136q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
227136.fw3 227136q1 \([0, 1, 0, -2084, -31290]\) \(3241792/567\) \(175155244992\) \([2]\) \(245760\) \(0.87727\) \(\Gamma_0(N)\)-optimal
227136.fw2 227136q2 \([0, 1, 0, -9689, 335271]\) \(5088448/441\) \(8718838861824\) \([2, 2]\) \(491520\) \(1.2238\)  
227136.fw1 227136q3 \([0, 1, 0, -151649, 22679775]\) \(2438569736/21\) \(3321462423552\) \([2]\) \(983040\) \(1.5704\)  
227136.fw4 227136q4 \([0, 1, 0, 10591, 1572351]\) \(830584/7203\) \(-1139261611278336\) \([2]\) \(983040\) \(1.5704\)  

Rank

sage: E.rank()
 

The elliptic curves in class 227136q have rank \(1\).

Complex multiplication

The elliptic curves in class 227136q do not have complex multiplication.

Modular form 227136.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} - q^{7} + q^{9} + 4 q^{11} - 2 q^{15} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.