Properties

Label 62400.f
Number of curves $4$
Conductor $62400$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62400.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.f1 62400bi4 \([0, -1, 0, -832033, 292395937]\) \(31103978031362/195\) \(399360000000\) \([4]\) \(589824\) \(1.8317\)  
62400.f2 62400bi3 \([0, -1, 0, -72033, 755937]\) \(20183398562/11567205\) \(23689635840000000\) \([2]\) \(589824\) \(1.8317\)  
62400.f3 62400bi2 \([0, -1, 0, -52033, 4575937]\) \(15214885924/38025\) \(38937600000000\) \([2, 2]\) \(294912\) \(1.4851\)  
62400.f4 62400bi1 \([0, -1, 0, -2033, 125937]\) \(-3631696/24375\) \(-6240000000000\) \([2]\) \(147456\) \(1.1385\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 62400.f have rank \(2\).

Complex multiplication

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

Modular form 62400.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4q^{7} + q^{9} - 4q^{11} + q^{13} - 6q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.