Properties

Label 35739a
Number of curves $1$
Conductor $35739$
CM no
Rank $1$

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

Elliptic curves in class 35739a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35739.m1 35739a1 \([0, 0, 1, -1481544, 1688080493]\) \(-56623104/161051\) \(-1022909299376557763907\) \([]\) \(1368000\) \(2.7185\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 35739a1 has rank \(1\).

Complex multiplication

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

Modular form 35739.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} + 2 q^{5} + 2 q^{7} - q^{11} + 5 q^{13} + 4 q^{16} - 3 q^{17} + O(q^{20})\) Copy content Toggle raw display