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Properties

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

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Show commands: SageMath
E = EllipticCurve("ga1")
 
E.isogeny_class()
 

Elliptic curves in class 303450ga

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.ga1 303450ga1 \([1, 0, 0, -1232013, 523414017]\) \(4386781853/27216\) \(1283062652156250000\) \([2]\) \(6656000\) \(2.3127\) \(\Gamma_0(N)\)-optimal
303450.ga2 303450ga2 \([1, 0, 0, -509513, 1132481517]\) \(-310288733/11573604\) \(-545622392829445312500\) \([2]\) \(13312000\) \(2.6592\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 303450.2.a.ga

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