Properties

Label 2400.j
Number of curves $4$
Conductor $2400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2400.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2400.j1 2400r3 \([0, -1, 0, -2033, 35937]\) \(14526784/15\) \(960000000\) \([4]\) \(1536\) \(0.64145\)  
2400.j2 2400r2 \([0, -1, 0, -1408, -19688]\) \(38614472/405\) \(3240000000\) \([2]\) \(1536\) \(0.64145\)  
2400.j3 2400r1 \([0, -1, 0, -158, 312]\) \(438976/225\) \(225000000\) \([2, 2]\) \(768\) \(0.29488\) \(\Gamma_0(N)\)-optimal
2400.j4 2400r4 \([0, -1, 0, 592, 1812]\) \(2863288/1875\) \(-15000000000\) \([2]\) \(1536\) \(0.64145\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2400.j have rank \(0\).

Complex multiplication

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

Modular form 2400.2.a.j

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.