Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 300.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
300.b1 300a2 [0, -1, 0, -1213, -15863] [] 108  
300.b2 300a1 [0, -1, 0, -13, -23] [] 36 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 300.2.a.b

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{7} + q^{9} + 6q^{11} - 5q^{13} + 6q^{17} + 5q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.