Properties

Label 4024.a
Number of curves $1$
Conductor $4024$
CM no
Rank $2$

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

Elliptic curves in class 4024.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4024.a1 4024b1 \([0, -1, 0, 12, 4]\) \(686000/503\) \(-128768\) \([]\) \(384\) \(-0.33122\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4024.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 4024.a do not have complex multiplication.

Modular form 4024.2.a.a

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