Properties

Label 72450.dg
Number of curves $2$
Conductor $72450$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("dg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72450.dg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.dg1 72450cy2 \([1, -1, 1, -3143180, -2121970553]\) \(89332607016927/1060723384\) \(40777770248578125000\) \([2]\) \(2211840\) \(2.5745\)  
72450.dg2 72450cy1 \([1, -1, 1, -38180, -85090553]\) \(-160103007/81288256\) \(-3124993638375000000\) \([2]\) \(1105920\) \(2.2279\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 72450.dg have rank \(0\).

Complex multiplication

The elliptic curves in class 72450.dg do not have complex multiplication.

Modular form 72450.2.a.dg

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} + 2q^{11} - 2q^{13} - q^{14} + q^{16} - 2q^{17} - 4q^{19} + O(q^{20})\)  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.