Properties

Label 72450cm
Number of curves $2$
Conductor $72450$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("cm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72450cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.cs1 72450cm1 \([1, -1, 1, -1108485380, 5939475630247]\) \(489781415227546051766883/233890092903563264000\) \(71932167165950558208000000000\) \([2]\) \(74317824\) \(4.2310\) \(\Gamma_0(N)\)-optimal
72450.cs2 72450cm2 \([1, -1, 1, 3978746620, 45172208814247]\) \(22649115256119592694355357/15973509811739648000000\) \(-4912603025382367056000000000000\) \([2]\) \(148635648\) \(4.5776\)  

Rank

sage: E.rank()
 

The elliptic curves in class 72450cm have rank \(1\).

Complex multiplication

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

Modular form 72450.2.a.cm

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} - 2q^{11} + 6q^{13} - q^{14} + q^{16} - 6q^{17} + O(q^{20})\)  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 Cremona 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 Cremona labels.