Properties

Label 302016.gw
Number of curves $4$
Conductor $302016$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gw1")
 
E.isogeny_class()
 

Elliptic curves in class 302016.gw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
302016.gw1 302016gw3 \([0, 1, 0, -147297, 21176703]\) \(3044193988/85293\) \(9902604443516928\) \([2]\) \(2949120\) \(1.8484\)  
302016.gw2 302016gw2 \([0, 1, 0, -21457, -744625]\) \(37642192/13689\) \(397326721499136\) \([2, 2]\) \(1474560\) \(1.5018\)  
302016.gw3 302016gw1 \([0, 1, 0, -19037, -1017117]\) \(420616192/117\) \(212247180288\) \([2]\) \(737280\) \(1.1552\) \(\Gamma_0(N)\)-optimal
302016.gw4 302016gw4 \([0, 1, 0, 65663, -5187745]\) \(269676572/257049\) \(-29843651525935104\) \([2]\) \(2949120\) \(1.8484\)  

Rank

sage: E.rank()
 

The elliptic curves in class 302016.gw have rank \(0\).

Complex multiplication

The elliptic curves in class 302016.gw do not have complex multiplication.

Modular form 302016.2.a.gw

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