Properties

Label 99856k
Number of curves $1$
Conductor $99856$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 99856k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
99856.e1 99856k1 \([0, -1, 0, -351576, 75679984]\) \(4826809/316\) \(314636844829229056\) \([]\) \(1198080\) \(2.1073\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 99856k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 99856k do not have complex multiplication.

Modular form 99856.2.a.k

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