Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62400.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.t1 62400fg4 \([0, -1, 0, -165633, 25903137]\) \(490757540836/2142075\) \(2193484800000000\) \([2]\) \(589824\) \(1.7966\)  
62400.t2 62400fg2 \([0, -1, 0, -15633, -46863]\) \(1650587344/950625\) \(243360000000000\) \([2, 2]\) \(294912\) \(1.4500\)  
62400.t3 62400fg1 \([0, -1, 0, -11133, -447363]\) \(9538484224/26325\) \(421200000000\) \([2]\) \(147456\) \(1.1035\) \(\Gamma_0(N)\)-optimal
62400.t4 62400fg3 \([0, -1, 0, 62367, -436863]\) \(26198797244/15234375\) \(-15600000000000000\) \([2]\) \(589824\) \(1.7966\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 62400.2.a.t

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.