Properties

Label 417450a
Number of curves $1$
Conductor $417450$
CM no
Rank $2$

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

Elliptic curves in class 417450a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
417450.a1 417450a1 \([1, 1, 0, -839500, -293066000]\) \(19535526241/253920\) \(850468860367500000\) \([]\) \(11151360\) \(2.2484\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 417450a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 417450a do not have complex multiplication.

Modular form 417450.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 5 q^{7} - q^{8} + q^{9} - q^{12} - q^{13} + 5 q^{14} + q^{16} - q^{17} - q^{18} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display