Properties

Label 109.a
Number of curves $1$
Conductor $109$
CM no
Rank $0$

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

Elliptic curves in class 109.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
109.a1 109a1 \([1, -1, 0, -8, -7]\) \(-60698457/109\) \(-109\) \([]\) \(4\) \(-0.71668\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 109.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 109.a do not have complex multiplication.

Modular form 109.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 3 q^{5} + 2 q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + q^{11} + 2 q^{14} - q^{16} - 8 q^{17} - 3 q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display