Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 205350.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
205350.b1 205350dt1 \([1, 1, 0, -4135, -97355]\) \(166942705/12288\) \(575742259200\) \([]\) \(331776\) \(1.0026\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 205350.b1 has rank \(1\).

Complex multiplication

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

Modular form 205350.2.a.b

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