Properties

Label 2320.f
Number of curves $4$
Conductor $2320$
CM no
Rank $1$
Graph

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

Elliptic curves in class 2320.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2320.f1 2320d3 \([0, 0, 0, -827, 7546]\) \(61085802564/11328125\) \(11600000000\) \([4]\) \(1024\) \(0.64940\)  
2320.f2 2320d2 \([0, 0, 0, -247, -1386]\) \(6509904336/525625\) \(134560000\) \([2, 2]\) \(512\) \(0.30283\)  
2320.f3 2320d1 \([0, 0, 0, -242, -1449]\) \(97960237056/725\) \(11600\) \([2]\) \(256\) \(-0.043745\) \(\Gamma_0(N)\)-optimal
2320.f4 2320d4 \([0, 0, 0, 253, -6286]\) \(1748981916/17682025\) \(-18106393600\) \([4]\) \(1024\) \(0.64940\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2320.f have rank \(1\).

Complex multiplication

The elliptic curves in class 2320.f do not have complex multiplication.

Modular form 2320.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{5} - 3 q^{9} - 2 q^{13} - 6 q^{17} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.