Properties

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

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("gh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 303450.gh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.gh1 303450gh2 \([1, 0, 0, -2532513, -1641484983]\) \(-7620530425/526848\) \(-124187792505000000000\) \([]\) \(16329600\) \(2.6066\)  
303450.gh2 303450gh1 \([1, 0, 0, 176862, -2313108]\) \(2595575/1512\) \(-356406292265625000\) \([]\) \(5443200\) \(2.0573\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 303450.2.a.gh

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