Properties

Label 62400.r
Number of curves $4$
Conductor $62400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 62400.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.r1 62400bh4 \([0, -1, 0, -33183233, 73585358337]\) \(986551739719628473/111045168\) \(454841008128000000\) \([2]\) \(3932160\) \(2.8125\)  
62400.r2 62400bh3 \([0, -1, 0, -3743233, -944177663]\) \(1416134368422073/725251155408\) \(2970628732551168000000\) \([2]\) \(3932160\) \(2.8125\)  
62400.r3 62400bh2 \([0, -1, 0, -2079233, 1144142337]\) \(242702053576633/2554695936\) \(10464034553856000000\) \([2, 2]\) \(1966080\) \(2.4659\)  
62400.r4 62400bh1 \([0, -1, 0, -31233, 44366337]\) \(-822656953/207028224\) \(-847987605504000000\) \([2]\) \(983040\) \(2.1194\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 62400.r have rank \(0\).

Complex multiplication

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

Modular form 62400.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} + 4 q^{11} + q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20})\) 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 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.