Properties

Label 218709b
Number of curves $1$
Conductor $218709$
CM no
Rank $0$

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

Elliptic curves in class 218709b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
218709.b1 218709b1 \([1, -1, 0, -396, -2943]\) \(-9434056897/24301\) \(-17715429\) \([]\) \(86016\) \(0.26699\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 218709b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 218709b do not have complex multiplication.

Modular form 218709.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 2 q^{5} - 4 q^{7} - 3 q^{8} + 2 q^{10} + 5 q^{11} - q^{13} - 4 q^{14} - q^{16} + 7 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display