Properties

Label 300.a
Number of curves $2$
Conductor $300$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 300.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
300.a1 300d1 \([0, -1, 0, -13, 22]\) \(131072/9\) \(18000\) \([2]\) \(24\) \(-0.43525\) \(\Gamma_0(N)\)-optimal
300.a2 300d2 \([0, -1, 0, 12, 72]\) \(5488/81\) \(-2592000\) \([2]\) \(48\) \(-0.088679\)  

Rank

sage: E.rank()
 

The elliptic curves in class 300.a have rank \(1\).

Complex multiplication

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

Modular form 300.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.