Properties

Label 62400ff
Number of curves $4$
Conductor $62400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ff1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62400ff

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62400.m4 62400ff1 [0, -1, 0, 326092, -51090438] [2] 1179648 \(\Gamma_0(N)\)-optimal
62400.m3 62400ff2 [0, -1, 0, -1627033, -451481063] [2, 2] 2359296  
62400.m2 62400ff3 [0, -1, 0, -11752033, 15191643937] [4] 4718592  
62400.m1 62400ff4 [0, -1, 0, -22752033, -41750856063] [2] 4718592  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 62400.2.a.ff

sage: E.q_eigenform(10)
 
\( q - q^{3} - 4q^{7} + q^{9} + q^{13} - 2q^{17} - 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.