Properties

Label 355740.du
Number of curves $2$
Conductor $355740$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("du1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 355740.du

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
355740.du1 355740du2 \([0, 1, 0, -3061340, 2056996500]\) \(59466754384/121275\) \(6470764581195129600\) \([2]\) \(11059200\) \(2.4960\)  
355740.du2 355740du1 \([0, 1, 0, -126485, 54251448]\) \(-67108864/343035\) \(-1143938738461281840\) \([2]\) \(5529600\) \(2.1494\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 355740.du have rank \(0\).

Complex multiplication

The elliptic curves in class 355740.du do not have complex multiplication.

Modular form 355740.2.a.du

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} - 6q^{13} + q^{15} + 2q^{17} + O(q^{20})\)  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.