Properties

Label 19110.a
Number of curves $1$
Conductor $19110$
CM no
Rank $1$

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

Elliptic curves in class 19110.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.a1 19110a1 \([1, 1, 0, 53287, -19722807]\) \(2902621910951/30895312500\) \(-178105328395312500\) \([]\) \(225792\) \(1.9911\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19110.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 19110.a do not have complex multiplication.

Modular form 19110.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - q^{11} - q^{12} - q^{13} + q^{15} + q^{16} - 3 q^{17} - q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display