Properties

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

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Show commands: SageMath
E = EllipticCurve("cc1")
 
E.isogeny_class()
 

Elliptic curves in class 336336cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
336336.cc2 336336cc1 \([0, -1, 0, 1552, 29184]\) \(857375/1287\) \(-620192821248\) \([2]\) \(393216\) \(0.94816\) \(\Gamma_0(N)\)-optimal
336336.cc1 336336cc2 \([0, -1, 0, -10208, 302016]\) \(244140625/61347\) \(29562524479488\) \([2]\) \(786432\) \(1.2947\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 336336.2.a.cc

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - q^{11} - q^{13} + 4 q^{17} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.