Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("fs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62400fs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62400.q2 62400fs1 [0, -1, 0, -569473, 165597217] [2] 589824 \(\Gamma_0(N)\)-optimal
62400.q1 62400fs2 [0, -1, 0, -582273, 157776417] [2] 1179648  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 62400.2.a.fs

sage: E.q_eigenform(10)
 
\( q - q^{3} - 4q^{7} + q^{9} + 2q^{11} - q^{13} + 4q^{17} + 2q^{19} + O(q^{20}) \)

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.