Properties

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

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72450.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.w1 72450a1 \([1, -1, 0, -123165042, -219939523884]\) \(489781415227546051766883/233890092903563264000\) \(98672382943690752000000000\) \([2]\) \(24772608\) \(3.6817\) \(\Gamma_0(N)\)-optimal
72450.w2 72450a2 \([1, -1, 0, 442082958, -1673192131884]\) \(22649115256119592694355357/15973509811739648000000\) \(-6738824451827664000000000000\) \([2]\) \(49545216\) \(4.0283\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 72450.2.a.w

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 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.