Properties

Label 333270.en
Number of curves $2$
Conductor $333270$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("en1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 333270.en

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.en1 333270en2 \([1, -1, 1, -2011622, 612666119]\) \(8341959848041/3327411150\) \(359088099123237753150\) \([2]\) \(16220160\) \(2.6424\)  
333270.en2 333270en1 \([1, -1, 1, -916592, -330811729]\) \(789145184521/17996580\) \(1942157855340262980\) \([2]\) \(8110080\) \(2.2958\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 333270.en have rank \(1\).

Complex multiplication

The elliptic curves in class 333270.en do not have complex multiplication.

Modular form 333270.2.a.en

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} + 2q^{11} - 2q^{13} - q^{14} + q^{16} + 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.