Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 35904.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35904.a1 35904g1 \([0, -1, 0, -12545, -536319]\) \(832972004929/610368\) \(160004308992\) \([2]\) \(73728\) \(1.0841\) \(\Gamma_0(N)\)-optimal
35904.a2 35904g2 \([0, -1, 0, -9985, -764159]\) \(-420021471169/727634952\) \(-190745136857088\) \([2]\) \(147456\) \(1.4307\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 35904.2.a.a

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