Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 300.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
300.c1 300b2 [0, 1, 0, -30333, -2043537] [] 540  
300.c2 300b1 [0, 1, 0, -333, -3537] [3] 180 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 300.2.a.c

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.