Properties

Label 8036.a
Number of curves $1$
Conductor $8036$
CM no
Rank $2$

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

Elliptic curves in class 8036.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8036.a1 8036b1 [0, -1, 0, -506, 4537] [] 2448 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8036.a1 has rank \(2\).

Complex multiplication

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

Modular form 8036.2.a.a

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