Properties

Label 336336bj
Number of curves $2$
Conductor $336336$
CM no
Rank $1$
Graph

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

Elliptic curves in class 336336bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
336336.bj2 336336bj1 \([0, -1, 0, -1160336, 481470144]\) \(860833894093732321/8282804244\) \(1662391942987776\) \([]\) \(3838464\) \(2.0821\) \(\Gamma_0(N)\)-optimal
336336.bj1 336336bj2 \([0, -1, 0, -37400176, -87999230528]\) \(28826282175168869972161/9077387406557184\) \(1821867962045653057536\) \([]\) \(26869248\) \(3.0551\)  

Rank

sage: E.rank()
 

The elliptic curves in class 336336bj have rank \(1\).

Complex multiplication

The elliptic curves in class 336336bj do not have complex multiplication.

Modular form 336336.2.a.bj

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - q^{11} - q^{13} + q^{15} - 3 q^{17} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.