Properties

Label 418.a
Number of curves $1$
Conductor $418$
CM no
Rank $1$

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

Elliptic curves in class 418.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
418.a1 418b1 \([1, 1, 1, 66, -5]\) \(31764658463/18833408\) \(-18833408\) \([]\) \(104\) \(0.085270\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 418.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 418.a do not have complex multiplication.

Modular form 418.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 2 q^{5} - q^{6} - 3 q^{7} + q^{8} - 2 q^{9} - 2 q^{10} - q^{11} - q^{12} + q^{13} - 3 q^{14} + 2 q^{15} + q^{16} - 7 q^{17} - 2 q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display