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Properties

Label 303450p
Number of curves $2$
Conductor $303450$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 303450p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
303450.p2 303450p1 [1, 1, 0, 14572675, -340918807875] [] 105753600 \(\Gamma_0(N)\)-optimal
303450.p1 303450p2 [1, 1, 0, -3274066700, -72122050446000] [] 317260800  

Rank

sage: E.rank()
 

The elliptic curves in class 303450p have rank \(0\).

Complex multiplication

The elliptic curves in class 303450p do not have complex multiplication.

Modular form 303450.2.a.p

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 3q^{11} - q^{12} - 4q^{13} + q^{14} + q^{16} - q^{18} + 8q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.