Properties

Label 174.a
Number of curves $1$
Conductor $174$
CM no
Rank $0$

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

Elliptic curves in class 174.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
174.a1 174e1 \([1, 1, 0, -56, -192]\) \(-19968681097/712704\) \(-712704\) \([]\) \(52\) \(-0.10484\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 174.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 174.a do not have complex multiplication.

Modular form 174.2.a.a

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