Properties

Label 99705.a
Number of curves $1$
Conductor $99705$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 99705.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
99705.a1 99705e1 \([0, -1, 1, -28996, 2169702]\) \(-111701610496/18862875\) \(-455303946850875\) \([]\) \(992256\) \(1.5394\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 99705.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 99705.a do not have complex multiplication.

Modular form 99705.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} - q^{5} + 2 q^{6} + 5 q^{7} + q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} - 10 q^{14} + q^{15} - 4 q^{16} - 2 q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display