Properties

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

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Show commands: SageMath
E = EllipticCurve("fr1")
 
E.isogeny_class()
 

Elliptic curves in class 62400.fr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.fr1 62400gc4 \([0, 1, 0, -773633, 261604863]\) \(12501706118329/2570490\) \(10528727040000000\) \([2]\) \(589824\) \(2.0715\)  
62400.fr2 62400gc2 \([0, 1, 0, -53633, 3124863]\) \(4165509529/1368900\) \(5607014400000000\) \([2, 2]\) \(294912\) \(1.7249\)  
62400.fr3 62400gc1 \([0, 1, 0, -21633, -1195137]\) \(273359449/9360\) \(38338560000000\) \([2]\) \(147456\) \(1.3783\) \(\Gamma_0(N)\)-optimal
62400.fr4 62400gc3 \([0, 1, 0, 154367, 21636863]\) \(99317171591/106616250\) \(-436700160000000000\) \([2]\) \(589824\) \(2.0715\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 62400.2.a.fr

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