Properties

Label 35739.p
Number of curves $1$
Conductor $35739$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 35739.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35739.p1 35739p1 \([1, -1, 0, -495, -3146]\) \(51026761/11979\) \(3152501451\) \([]\) \(17280\) \(0.53438\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 35739.p1 has rank \(1\).

Complex multiplication

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

Modular form 35739.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - q^{5} - 3 q^{7} - 3 q^{8} - q^{10} - q^{11} - 6 q^{13} - 3 q^{14} - q^{16} + O(q^{20})\) Copy content Toggle raw display