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Properties

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

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Show commands: SageMath
E = EllipticCurve("gz1")
 
E.isogeny_class()
 

Elliptic curves in class 303450.gz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.gz1 303450gz2 \([1, 0, 0, -130962668, -576976403568]\) \(-4928752745352265/1056964608\) \(-53270855067961707724800\) \([]\) \(63452160\) \(3.3557\)  
303450.gz2 303450gz1 \([1, 0, 0, 582907, -2727350463]\) \(434602535/64012032\) \(-3226196651683655059200\) \([]\) \(21150720\) \(2.8064\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 303450.2.a.gz

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.