Properties

Label 4015.a
Number of curves $1$
Conductor $4015$
CM no
Rank $1$

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

Elliptic curves in class 4015.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4015.a1 4015a1 \([0, -1, 1, -1, 7]\) \(-262144/20075\) \(-20075\) \([]\) \(200\) \(-0.49471\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4015.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4015.a do not have complex multiplication.

Modular form 4015.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} - q^{5} - 3 q^{7} - 2 q^{9} + q^{11} + 2 q^{12} + q^{13} + q^{15} + 4 q^{16} - 3 q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display