Properties

Label 327990.d
Number of curves $4$
Conductor $327990$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 327990.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.d1 327990d4 \([1, 1, 0, -1005853, -368944997]\) \(189208196468929/10860320250\) \(6459971758228550250\) \([2]\) \(7257600\) \(2.3635\)  
327990.d2 327990d2 \([1, 1, 0, -173263, 27564637]\) \(967068262369/4928040\) \(2931313118820840\) \([2]\) \(2419200\) \(1.8142\)  
327990.d3 327990d1 \([1, 1, 0, -5063, 888117]\) \(-24137569/561600\) \(-334052777073600\) \([2]\) \(1209600\) \(1.4676\) \(\Gamma_0(N)\)-optimal
327990.d4 327990d3 \([1, 1, 0, 45397, -23504247]\) \(17394111071/411937500\) \(-245030031794437500\) \([2]\) \(3628800\) \(2.0169\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 327990.2.a.d

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.