Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62400.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.l1 62400bg4 \([0, -1, 0, -30433, -1983263]\) \(3044193988/85293\) \(87340032000000\) \([2]\) \(262144\) \(1.4541\)  
62400.l2 62400bg2 \([0, -1, 0, -4433, 70737]\) \(37642192/13689\) \(3504384000000\) \([2, 2]\) \(131072\) \(1.1076\)  
62400.l3 62400bg1 \([0, -1, 0, -3933, 96237]\) \(420616192/117\) \(1872000000\) \([2]\) \(65536\) \(0.76098\) \(\Gamma_0(N)\)-optimal
62400.l4 62400bg3 \([0, -1, 0, 13567, 484737]\) \(269676572/257049\) \(-263218176000000\) \([2]\) \(262144\) \(1.4541\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 62400.2.a.l

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