Properties

Label 327.a
Number of curves $1$
Conductor $327$
CM no
Rank $1$

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

Elliptic curves in class 327.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327.a1 327a1 \([1, 0, 0, 4, -3]\) \(6967871/8829\) \(-8829\) \([]\) \(16\) \(-0.55685\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 327.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 327.a do not have complex multiplication.

Modular form 327.2.a.a

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