Properties

Label 57038p
Number of curves $1$
Conductor $57038$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 57038p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57038.m1 57038p1 \([1, 0, 0, -1271, -16531]\) \(4826809/316\) \(14866498396\) \([]\) \(52416\) \(0.70165\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 57038p1 has rank \(0\).

Complex multiplication

The elliptic curves in class 57038p do not have complex multiplication.

Modular form 57038.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} - 3 q^{7} + q^{8} - 2 q^{9} - q^{10} + 4 q^{11} + q^{12} + 7 q^{13} - 3 q^{14} - q^{15} + q^{16} - 4 q^{17} - 2 q^{18} + O(q^{20})\) Copy content Toggle raw display