Properties

Label 157170.ba
Number of curves $1$
Conductor $157170$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 157170.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
157170.ba1 157170ct1 \([1, 0, 1, -589814, 220931336]\) \(-4701189640361761/1649907792000\) \(-7963789779595728000\) \([]\) \(4064256\) \(2.3379\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 157170.ba1 has rank \(1\).

Complex multiplication

The elliptic curves in class 157170.ba do not have complex multiplication.

Modular form 157170.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 3 q^{7} - q^{8} + q^{9} + q^{10} + q^{11} + q^{12} - 3 q^{14} - q^{15} + q^{16} - 6 q^{17} - q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display