Properties

Label 259182.a
Number of curves $1$
Conductor $259182$
CM no
Rank $1$

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

Elliptic curves in class 259182.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.a1 259182a1 \([1, -1, 0, 1633296, -5027953276]\) \(1672076814404733/38858425153436\) \(-11198174447182277817108\) \([]\) \(27751680\) \(2.9111\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 259182.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 259182.a do not have complex multiplication.

Modular form 259182.2.a.a

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