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Properties

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

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Show commands: SageMath
E = EllipticCurve("gm1")
 
E.isogeny_class()
 

Elliptic curves in class 303450.gm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.gm1 303450gm2 \([1, 0, 0, -1708013, 859096017]\) \(-287137850384705/22020096\) \(-42259660800000000\) \([]\) \(5760000\) \(2.2384\)  
303450.gm2 303450gm1 \([1, 0, 0, 14512, 109392]\) \(110072002975/65345616\) \(-200651882130000\) \([]\) \(1152000\) \(1.4337\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 303450.2.a.gm

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} + q^{12} - 4 q^{13} + q^{14} + q^{16} + q^{18} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.