Properties

Label 57.a
Number of curves $1$
Conductor $57$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 57.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57.a1 57a1 \([0, -1, 1, -2, 2]\) \(-1404928/171\) \(-171\) \([]\) \(4\) \(-0.83655\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 57.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 57.a do not have complex multiplication.

Modular form 57.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} + q^{9} + 6 q^{10} + q^{11} - 2 q^{12} + 2 q^{13} + 10 q^{14} + 3 q^{15} - 4 q^{16} - q^{17} - 2 q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display