Properties

Label 249090.a
Number of curves $1$
Conductor $249090$
CM no
Rank $1$

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

Elliptic curves in class 249090.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
249090.a1 249090a1 \([1, 1, 0, -3657917703, -68886400846347]\) \(882855229481914983409/176566071214080000\) \(1082538281493134334341038080000\) \([]\) \(650795904\) \(4.4792\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 249090.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 249090.a do not have complex multiplication.

Modular form 249090.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} - 4 q^{11} - q^{12} + 6 q^{13} + 4 q^{14} + q^{15} + q^{16} + q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display