Properties

Label 416955.bf
Number of curves $1$
Conductor $416955$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 416955.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
416955.bf1 416955bf1 \([0, -1, 1, 196625, -17574219]\) \(17869652393984/13156171875\) \(-618943696446796875\) \([]\) \(5630688\) \(2.1022\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 416955.bf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 416955.bf do not have complex multiplication.

Modular form 416955.2.a.bf

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