Properties

Label 2310.f
Number of curves $4$
Conductor $2310$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2310.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.f1 2310f4 \([1, 0, 1, -26044, 1615406]\) \(1953542217204454969/170843779260\) \(170843779260\) \([2]\) \(5120\) \(1.1966\)  
2310.f2 2310f3 \([1, 0, 1, -9444, -335954]\) \(93137706732176569/5369647977540\) \(5369647977540\) \([2]\) \(5120\) \(1.1966\)  
2310.f3 2310f2 \([1, 0, 1, -1744, 21326]\) \(586145095611769/140040608400\) \(140040608400\) \([2, 2]\) \(2560\) \(0.85005\)  
2310.f4 2310f1 \([1, 0, 1, 256, 2126]\) \(1865864036231/2993760000\) \(-2993760000\) \([2]\) \(1280\) \(0.50348\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2310.f have rank \(1\).

Complex multiplication

The elliptic curves in class 2310.f do not have complex multiplication.

Modular form 2310.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + q^{11} + q^{12} - 2 q^{13} + q^{14} - q^{15} + q^{16} - 2 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.