Properties

Label 471510.b
Number of curves $1$
Conductor $471510$
CM no
Rank $1$

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

Elliptic curves in class 471510.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
471510.b1 471510b1 \([1, -1, 0, 1573134525, 632871536251761]\) \(4284106395540116951/1724166870117187500\) \(-173276771375156912155151367187500\) \([]\) \(1675395072\) \(4.8651\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 471510.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 471510.b do not have complex multiplication.

Modular form 471510.2.a.b

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