Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62400a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.cp3 62400a1 \([0, -1, 0, -6508, 204262]\) \(30488290624/195\) \(195000000\) \([2]\) \(36864\) \(0.77535\) \(\Gamma_0(N)\)-optimal
62400.cp2 62400a2 \([0, -1, 0, -6633, 196137]\) \(504358336/38025\) \(2433600000000\) \([2, 2]\) \(73728\) \(1.1219\)  
62400.cp4 62400a3 \([0, -1, 0, 6367, 859137]\) \(55742968/658125\) \(-336960000000000\) \([2]\) \(147456\) \(1.4685\)  
62400.cp1 62400a4 \([0, -1, 0, -21633, -988863]\) \(2186875592/428415\) \(219348480000000\) \([2]\) \(147456\) \(1.4685\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 62400.2.a.a

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