Properties

Label 8032.d
Number of curves $1$
Conductor $8032$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 8032.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8032.d1 8032d1 \([0, 0, 0, -53752, 4796688]\) \(-4193219998665216/15813251\) \(-64771076096\) \([]\) \(15840\) \(1.2894\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8032.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8032.d do not have complex multiplication.

Modular form 8032.2.a.d

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