Properties

Label 308550.do
Number of curves $2$
Conductor $308550$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("do1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 308550.do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308550.do1 308550do2 \([1, 0, 1, -434151, -70367552]\) \(326940373369/112003650\) \(3100332784338281250\) \([2]\) \(5898240\) \(2.2501\)  
308550.do2 308550do1 \([1, 0, 1, 80099, -7629052]\) \(2053225511/2098140\) \(-58077859320937500\) \([2]\) \(2949120\) \(1.9035\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 308550.do have rank \(0\).

Complex multiplication

The elliptic curves in class 308550.do do not have complex multiplication.

Modular form 308550.2.a.do

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - 2q^{7} - q^{8} + q^{9} + q^{12} + 2q^{14} + q^{16} + q^{17} - q^{18} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.