Properties

Label 214.a
Number of curves $1$
Conductor $214$
CM no
Rank $1$

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

Elliptic curves in class 214.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
214.a1 214b1 \([1, 0, 1, 1, 0]\) \(357911/214\) \(-214\) \([]\) \(12\) \(-0.86354\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 214.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 214.a do not have complex multiplication.

Modular form 214.2.a.a

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