Properties

Label 1573.b
Number of curves $1$
Conductor $1573$
CM no
Rank $1$

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

Elliptic curves in class 1573.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1573.b1 1573b1 \([0, -1, 1, -161, 2925]\) \(-262144/1859\) \(-3293331899\) \([]\) \(480\) \(0.50945\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1573.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1573.b do not have complex multiplication.

Modular form 1573.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} - q^{5} + 2 q^{7} - 2 q^{9} + 2 q^{12} + q^{13} + q^{15} + 4 q^{16} + 4 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display