Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("hg1")
 
E.isogeny_class()
 

Elliptic curves in class 303450hg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.hg2 303450hg1 \([1, 0, 0, 36697, 15716157]\) \(9056932295/181997172\) \(-109824232423871700\) \([]\) \(3732480\) \(1.9502\) \(\Gamma_0(N)\)-optimal
303450.hg1 303450hg2 \([1, 0, 0, -331778, -435223548]\) \(-6693187811305/131714173248\) \(-79481498626288852800\) \([]\) \(11197440\) \(2.4995\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 303450.2.a.hg

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 Cremona 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 Cremona labels.