Properties

Label 4029.a
Number of curves $1$
Conductor $4029$
CM no
Rank $1$

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

Elliptic curves in class 4029.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4029.a1 4029b1 \([0, 1, 1, -17, -10]\) \(575930368/326349\) \(326349\) \([]\) \(480\) \(-0.25208\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4029.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4029.a do not have complex multiplication.

Modular form 4029.2.a.a

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