Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35904g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35904.a1 35904g1 [0, -1, 0, -12545, -536319] [2] 73728 \(\Gamma_0(N)\)-optimal
35904.a2 35904g2 [0, -1, 0, -9985, -764159] [2] 147456  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 35904.2.a.g

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

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 Cremona 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 Cremona labels.