Properties

Label 8008.e
Number of curves $1$
Conductor $8008$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 8008.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8008.e1 8008d1 \([0, 0, 0, 32348, -4190188]\) \(14622648823378944/38090758396691\) \(-9751234149552896\) \([]\) \(59520\) \(1.7517\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8008.e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 8008.e do not have complex multiplication.

Modular form 8008.2.a.e

sage: E.q_eigenform(10)
 
\(q + 3 q^{3} + q^{5} + q^{7} + 6 q^{9} - q^{11} + q^{13} + 3 q^{15} + 4 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display