Properties

Label 250173.bf
Number of curves $1$
Conductor $250173$
CM no
Rank $1$

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

Elliptic curves in class 250173.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250173.bf1 250173bf1 \([0, 0, 1, 12231402, 15866470291]\) \(5900696781553664/6585747900963\) \(-225867755480590005800787\) \([]\) \(26956800\) \(3.1677\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 250173.bf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 250173.bf do not have complex multiplication.

Modular form 250173.2.a.bf

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