Properties

Label 62400.p
Number of curves $2$
Conductor $62400$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62400.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.p1 62400fr2 \([0, -1, 0, -24833, -482463]\) \(26463592/13689\) \(876096000000000\) \([2]\) \(286720\) \(1.5592\)  
62400.p2 62400fr1 \([0, -1, 0, -19833, -1067463]\) \(107850176/117\) \(936000000000\) \([2]\) \(143360\) \(1.2127\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 62400.p have rank \(1\).

Complex multiplication

The elliptic curves in class 62400.p do not have complex multiplication.

Modular form 62400.2.a.p

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