Properties

Label 2400.y
Number of curves $4$
Conductor $2400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2400.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2400.y1 2400bb2 \([0, 1, 0, -2033, -35937]\) \(14526784/15\) \(960000000\) \([2]\) \(1536\) \(0.64145\)  
2400.y2 2400bb3 \([0, 1, 0, -1408, 19688]\) \(38614472/405\) \(3240000000\) \([4]\) \(1536\) \(0.64145\)  
2400.y3 2400bb1 \([0, 1, 0, -158, -312]\) \(438976/225\) \(225000000\) \([2, 2]\) \(768\) \(0.29488\) \(\Gamma_0(N)\)-optimal
2400.y4 2400bb4 \([0, 1, 0, 592, -1812]\) \(2863288/1875\) \(-15000000000\) \([2]\) \(1536\) \(0.64145\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2400.y have rank \(1\).

Complex multiplication

The elliptic curves in class 2400.y do not have complex multiplication.

Modular form 2400.2.a.y

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.