Properties

Label 205350.bn
Number of curves $1$
Conductor $205350$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 205350.bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
205350.bn1 205350da1 \([1, 0, 1, 50624, -17019352]\) \(357911/3330\) \(-133497952218281250\) \([]\) \(2626560\) \(1.9673\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 205350.bn1 has rank \(2\).

Complex multiplication

The elliptic curves in class 205350.bn do not have complex multiplication.

Modular form 205350.2.a.bn

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