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Properties

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

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Show commands: SageMath
E = EllipticCurve("fg1")
 
E.isogeny_class()
 

Elliptic curves in class 303450fg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.fg2 303450fg1 \([1, 1, 1, -6491813, -59522280469]\) \(-16329068153/816480000\) \(-1512884834410477500000000\) \([2]\) \(60162048\) \(3.3196\) \(\Gamma_0(N)\)-optimal
303450.fg1 303450fg2 \([1, 1, 1, -271793813, -1714476156469]\) \(1198345620520313/8268750000\) \(15321460996633886718750000\) \([2]\) \(120324096\) \(3.6662\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 303450.2.a.fg

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