Properties

Label 100016.f
Number of curves $1$
Conductor $100016$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 100016.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100016.f1 100016f1 \([0, -1, 0, -35, 94]\) \(-304900096/6251\) \(-100016\) \([]\) \(7680\) \(-0.24896\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100016.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100016.f do not have complex multiplication.

Modular form 100016.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} - 2 q^{9} + 2 q^{11} + 4 q^{13} - q^{15} - 6 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display