Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2400.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2400.i1 2400a3 \([0, -1, 0, -4008, 99012]\) \(890277128/15\) \(120000000\) \([4]\) \(1536\) \(0.68052\)  
2400.i2 2400a2 \([0, -1, 0, -1008, -10488]\) \(14172488/1875\) \(15000000000\) \([2]\) \(1536\) \(0.68052\)  
2400.i3 2400a1 \([0, -1, 0, -258, 1512]\) \(1906624/225\) \(225000000\) \([2, 2]\) \(768\) \(0.33395\) \(\Gamma_0(N)\)-optimal
2400.i4 2400a4 \([0, -1, 0, 367, 7137]\) \(85184/405\) \(-25920000000\) \([2]\) \(1536\) \(0.68052\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2400.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 2 q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})\) Copy content 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.