Properties

Label 35739.t
Number of curves $4$
Conductor $35739$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 35739.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35739.t1 35739q4 \([1, -1, 0, -476046, 126416565]\) \(347873904937/395307\) \(13557625672660443\) \([2]\) \(345600\) \(2.0089\)  
35739.t2 35739q2 \([1, -1, 0, -37431, 884952]\) \(169112377/88209\) \(3025255315387041\) \([2, 2]\) \(172800\) \(1.6623\)  
35739.t3 35739q1 \([1, -1, 0, -21186, -1171665]\) \(30664297/297\) \(10186044832953\) \([2]\) \(86400\) \(1.3157\) \(\Gamma_0(N)\)-optimal
35739.t4 35739q3 \([1, -1, 0, 141264, 6781887]\) \(9090072503/5845851\) \(-200491920447013899\) \([2]\) \(345600\) \(2.0089\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35739.t have rank \(1\).

Complex multiplication

The elliptic curves in class 35739.t do not have complex multiplication.

Modular form 35739.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 2 q^{5} + 4 q^{7} - 3 q^{8} + 2 q^{10} - q^{11} + 2 q^{13} + 4 q^{14} - q^{16} + 2 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.