Properties

Label 292215bj
Number of curves $4$
Conductor $292215$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 292215bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
292215.bj3 292215bj1 \([1, 0, 1, -33883, -2396407]\) \(2428257525121/8150625\) \(14439329375625\) \([2]\) \(737280\) \(1.3894\) \(\Gamma_0(N)\)-optimal
292215.bj2 292215bj2 \([1, 0, 1, -49008, -49007]\) \(7347774183121/4251692025\) \(7532131775501025\) \([2, 2]\) \(1474560\) \(1.7360\)  
292215.bj1 292215bj3 \([1, 0, 1, -536033, 150539123]\) \(9614816895690721/34652610405\) \(61389213141692205\) \([2]\) \(2949120\) \(2.0825\)  
292215.bj4 292215bj4 \([1, 0, 1, 196017, -343037]\) \(470166844956479/272118787605\) \(-482075031488301405\) \([2]\) \(2949120\) \(2.0825\)  

Rank

sage: E.rank()
 

The elliptic curves in class 292215bj have rank \(1\).

Complex multiplication

The elliptic curves in class 292215bj do not have complex multiplication.

Modular form 292215.2.a.bj

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + q^{7} - 3 q^{8} + q^{9} + q^{10} - q^{12} - 2 q^{13} + q^{14} + q^{15} - q^{16} + 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.