Properties

Label 327990.l
Number of curves $2$
Conductor $327990$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 327990.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.l1 327990l1 \([1, 0, 1, -3343834, -2119930228]\) \(285020220941/31150080\) \(451898757719997419520\) \([2]\) \(14966784\) \(2.6970\) \(\Gamma_0(N)\)-optimal
327990.l2 327990l2 \([1, 0, 1, 4460646, -10542525044]\) \(676604913139/3701505600\) \(-53698282069696568366400\) \([2]\) \(29933568\) \(3.0435\)  

Rank

sage: E.rank()
 

The elliptic curves in class 327990.l have rank \(0\).

Complex multiplication

The elliptic curves in class 327990.l do not have complex multiplication.

Modular form 327990.2.a.l

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