Properties

Label 270480.gs
Number of curves $4$
Conductor $270480$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("gs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 270480.gs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.gs1 270480gs4 \([0, 1, 0, -9088536, -10549060236]\) \(344577854816148242/2716875\) \(654617859840000\) \([2]\) \(5898240\) \(2.4339\)  
270480.gs2 270480gs2 \([0, 1, 0, -568416, -164737980]\) \(168591300897604/472410225\) \(56912476734489600\) \([2, 2]\) \(2949120\) \(2.0873\)  
270480.gs3 270480gs3 \([0, 1, 0, -343016, -296461740]\) \(-18524646126002/146738831715\) \(-35356010111873095680\) \([2]\) \(5898240\) \(2.4339\)  
270480.gs4 270480gs1 \([0, 1, 0, -49996, -295156]\) \(458891455696/264449745\) \(7964735500673280\) \([2]\) \(1474560\) \(1.7407\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 270480.gs have rank \(0\).

Complex multiplication

The elliptic curves in class 270480.gs do not have complex multiplication.

Modular form 270480.2.a.gs

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} + 4 q^{11} - 2 q^{13} - q^{15} + 2 q^{17} - 4 q^{19} + O(q^{20})\)  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.