Properties

Label 468.d
Number of curves $2$
Conductor $468$
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 468.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
468.d1 468e2 \([0, 0, 0, -183, 830]\) \(3631696/507\) \(94618368\) \([2]\) \(192\) \(0.25678\)  
468.d2 468e1 \([0, 0, 0, -48, -115]\) \(1048576/117\) \(1364688\) \([2]\) \(96\) \(-0.089794\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 468.d have rank \(0\).

Complex multiplication

The elliptic curves in class 468.d do not have complex multiplication.

Modular form 468.2.a.d

sage: E.q_eigenform(10)
 
\(q + 4q^{5} - 2q^{7} + 4q^{11} + q^{13} - 2q^{17} - 2q^{19} + O(q^{20})\)  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.