Properties

Label 4014.b
Number of curves $1$
Conductor $4014$
CM no
Rank $2$

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

Elliptic curves in class 4014.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4014.b1 4014b1 \([1, -1, 0, 255, -451]\) \(92959677/57088\) \(-1123663104\) \([]\) \(2688\) \(0.42582\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4014.b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 4014.b do not have complex multiplication.

Modular form 4014.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 4 q^{7} - q^{8} + q^{10} - 2 q^{11} - 6 q^{13} + 4 q^{14} + q^{16} - 8 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display