Properties

Label 303450.cp
Number of curves $2$
Conductor $303450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cp1")
 
E.isogeny_class()
 

Elliptic curves in class 303450.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.cp1 303450cp2 \([1, 0, 1, -11328951, -14680505702]\) \(-4928752745352265/1056964608\) \(-34483883212800000000\) \([]\) \(18662400\) \(2.7439\)  
303450.cp2 303450cp1 \([1, 0, 1, 50424, -69388202]\) \(434602535/64012032\) \(-2088417548700000000\) \([3]\) \(6220800\) \(2.1946\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 303450.cp have rank \(1\).

Complex multiplication

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

Modular form 303450.2.a.cp

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.