Properties

Label 20280s
Number of curves $4$
Conductor $20280$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 20280s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20280.n4 20280s1 \([0, -1, 0, 14140, 452100]\) \(253012016/219375\) \(-271073593440000\) \([4]\) \(64512\) \(1.4570\) \(\Gamma_0(N)\)-optimal
20280.n3 20280s2 \([0, -1, 0, -70360, 4068700]\) \(7793764996/3080025\) \(15223493007590400\) \([2, 2]\) \(129024\) \(1.8036\)  
20280.n2 20280s3 \([0, -1, 0, -509760, -137066580]\) \(1481943889298/34543665\) \(341474658539489280\) \([2]\) \(258048\) \(2.1501\)  
20280.n1 20280s4 \([0, -1, 0, -982960, 375314380]\) \(10625310339698/3855735\) \(38115115826411520\) \([2]\) \(258048\) \(2.1501\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20280s have rank \(1\).

Complex multiplication

The elliptic curves in class 20280s do not have complex multiplication.

Modular form 20280.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - 4 q^{11} - q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.