Properties

Label 2280.a
Number of curves $4$
Conductor $2280$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2280.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2280.a1 2280b4 \([0, -1, 0, -30400, 2050300]\) \(3034301922374404/1425\) \(1459200\) \([2]\) \(2048\) \(0.95645\)  
2280.a2 2280b3 \([0, -1, 0, -2280, 18972]\) \(1280615525284/601171875\) \(615600000000\) \([2]\) \(2048\) \(0.95645\)  
2280.a3 2280b2 \([0, -1, 0, -1900, 32500]\) \(2964647793616/2030625\) \(519840000\) \([2, 2]\) \(1024\) \(0.60988\)  
2280.a4 2280b1 \([0, -1, 0, -95, 732]\) \(-5988775936/9774075\) \(-156385200\) \([4]\) \(512\) \(0.26330\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2280.a have rank \(1\).

Complex multiplication

The elliptic curves in class 2280.a do not have complex multiplication.

Modular form 2280.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - 2 q^{13} - q^{15} - 6 q^{17} + q^{19} + O(q^{20})\) 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.