Properties

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

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Show commands: SageMath
E = EllipticCurve("ey1")
 
E.isogeny_class()
 

Elliptic curves in class 62400ey

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.br2 62400ey1 \([0, -1, 0, -33, -48063]\) \(-4/975\) \(-998400000000\) \([2]\) \(73728\) \(0.98134\) \(\Gamma_0(N)\)-optimal
62400.br1 62400ey2 \([0, -1, 0, -20033, -1068063]\) \(434163602/7605\) \(15575040000000\) \([2]\) \(147456\) \(1.3279\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 62400.2.a.ey

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{7} + q^{9} + q^{13} + 4 q^{17} + 6 q^{19} + O(q^{20})\) Copy content 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.