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Properties

Label 35904.de
Number of curves $2$
Conductor $35904$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("de1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35904.de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35904.de1 35904ck1 [0, 1, 0, -57857, -5333505] [2] 215040 \(\Gamma_0(N)\)-optimal
35904.de2 35904ck2 [0, 1, 0, -16897, -12698113] [2] 430080  

Rank

sage: E.rank()
 

The elliptic curves in class 35904.de have rank \(1\).

Complex multiplication

The elliptic curves in class 35904.de do not have complex multiplication.

Modular form 35904.2.a.de

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{5} + 4q^{7} + q^{9} - q^{11} + 4q^{13} + 2q^{15} - q^{17} - 8q^{19} + O(q^{20}) \)

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.