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Properties

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

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 303450.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.x1 303450x2 \([1, 1, 0, -8294450, -54402943500]\) \(-6693187811305/131714173248\) \(-1241898416035763325000000\) \([]\) \(55987200\) \(3.3042\)  
303450.x2 303450x1 \([1, 1, 0, 917425, 1964519625]\) \(9056932295/181997172\) \(-1716003631622995312500\) \([]\) \(18662400\) \(2.7549\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 303450.2.a.x

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