Properties

Label 85544.b
Number of curves $1$
Conductor $85544$
CM no
Rank $2$

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

Elliptic curves in class 85544.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85544.b1 85544a1 \([0, 1, 0, -2697, 47867]\) \(351232/37\) \(228631053568\) \([]\) \(78848\) \(0.91437\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 85544.b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 85544.b do not have complex multiplication.

Modular form 85544.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{5} - q^{7} - 2 q^{9} - q^{11} - 6 q^{13} + 2 q^{15} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display