Properties

Label 327990.z
Number of curves $2$
Conductor $327990$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 327990.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.z1 327990z1 \([1, 1, 1, -53768091, 171055701513]\) \(-40861808665609/6406452000\) \(-2695240696190539296852000\) \([]\) \(65772000\) \(3.4163\) \(\Gamma_0(N)\)-optimal
327990.z2 327990z2 \([1, 1, 1, 359991294, -616907671281]\) \(12263649421047431/7488000000000\) \(-3150255762951905088000000000\) \([]\) \(197316000\) \(3.9656\)  

Rank

sage: E.rank()
 

The elliptic curves in class 327990.z have rank \(1\).

Complex multiplication

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

Modular form 327990.2.a.z

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.