Properties

Label 100773.a
Number of curves $1$
Conductor $100773$
CM no
Rank $2$

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

Elliptic curves in class 100773.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100773.a1 100773a1 \([1, -1, 0, -51, 44]\) \(20346417/11197\) \(8162613\) \([]\) \(29120\) \(0.016865\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100773.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 100773.a do not have complex multiplication.

Modular form 100773.2.a.a

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