Properties

Label 100018.b
Number of curves $1$
Conductor $100018$
CM no
Rank $0$

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

Elliptic curves in class 100018.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100018.b1 100018b1 \([1, 1, 0, -50, -172]\) \(-14260515625/1600288\) \(-1600288\) \([]\) \(26240\) \(-0.072382\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100018.b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 100018.b do not have complex multiplication.

Modular form 100018.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 2 q^{6} + 4 q^{7} - q^{8} + q^{9} - 5 q^{11} + 2 q^{12} - 3 q^{13} - 4 q^{14} + q^{16} - q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display