Properties

Label 8048.d
Number of curves $1$
Conductor $8048$
CM no
Rank $1$

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

Elliptic curves in class 8048.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8048.d1 8048j1 \([0, -1, 0, -24, -272]\) \(-389017/8048\) \(-32964608\) \([]\) \(1152\) \(0.12347\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8048.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8048.d do not have complex multiplication.

Modular form 8048.2.a.d

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