Properties

Label 8036.f
Number of curves $1$
Conductor $8036$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8036.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8036.f1 8036d1 \([0, 1, 0, -30, -43]\) \(3937024/1681\) \(1317904\) \([]\) \(576\) \(-0.12915\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8036.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8036.f do not have complex multiplication.

Modular form 8036.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 2q^{9} + 3q^{11} - 2q^{13} + q^{15} - q^{17} + 3q^{19} + O(q^{20})\)  Toggle raw display