Properties

Label 8016.d
Number of curves $2$
Conductor $8016$
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 8016.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8016.d1 8016c2 \([0, -1, 0, -5128, 143008]\) \(14566408766500/6777027\) \(6939675648\) \([2]\) \(7040\) \(0.84463\)  
8016.d2 8016c1 \([0, -1, 0, -268, 3040]\) \(-8346562000/9861183\) \(-2524462848\) \([2]\) \(3520\) \(0.49806\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8016.d have rank \(0\).

Complex multiplication

The elliptic curves in class 8016.d do not have complex multiplication.

Modular form 8016.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4q^{7} + q^{9} + 4q^{11} + 2q^{13} + 4q^{19} + O(q^{20})\)  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.