Properties

Label 300.d
Number of curves $2$
Conductor $300$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 300.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
300.d1 300c1 [0, 1, 0, -333, 2088] [2] 120 \(\Gamma_0(N)\)-optimal
300.d2 300c2 [0, 1, 0, 292, 9588] [2] 240  

Rank

sage: E.rank()
 

The elliptic curves in class 300.d have rank \(0\).

Complex multiplication

The elliptic curves in class 300.d do not have complex multiplication.

Modular form 300.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{3} + 4q^{7} + q^{9} - 4q^{11} + 4q^{17} + O(q^{20})\)  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.