Properties

Label 10008.d
Number of curves $1$
Conductor $10008$
CM no
Rank $1$

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

Elliptic curves in class 10008.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10008.d1 10008c1 \([0, 0, 0, 117, 54]\) \(237276/139\) \(-103762944\) \([]\) \(2048\) \(0.22754\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10008.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 10008.d do not have complex multiplication.

Modular form 10008.2.a.d

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