Properties

Label 8001.b
Number of curves $1$
Conductor $8001$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 8001.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8001.b1 8001b1 \([0, 0, 1, -33, 70]\) \(147197952/6223\) \(168021\) \([]\) \(1216\) \(-0.23285\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8001.b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 8001.b do not have complex multiplication.

Modular form 8001.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} - q^{5} - q^{7} + 2 q^{10} - q^{13} + 2 q^{14} - 4 q^{16} - 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display