Properties

Label 333270.dh
Number of curves $2$
Conductor $333270$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("dh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 333270.dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.dh1 333270dh1 \([1, -1, 1, -6071168, -5646794093]\) \(8493409990827/185150000\) \(539488293150073050000\) \([2]\) \(16220160\) \(2.7664\) \(\Gamma_0(N)\)-optimal
333270.dh2 333270dh2 \([1, -1, 1, 499012, -17231335469]\) \(4716275733/44023437500\) \(-128275069702802695312500\) \([2]\) \(32440320\) \(3.1129\)  

Rank

sage: E.rank()
 

The elliptic curves in class 333270.dh have rank \(1\).

Complex multiplication

The elliptic curves in class 333270.dh do not have complex multiplication.

Modular form 333270.2.a.dh

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} + 2q^{11} + 2q^{13} - q^{14} + q^{16} + 2q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.