Properties

Label 171.d
Number of curves $1$
Conductor $171$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 171.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
171.d1 171d1 \([0, 0, 1, -21, -41]\) \(-1404928/171\) \(-124659\) \([]\) \(32\) \(-0.28724\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 171.d1 has rank \(0\).

Complex multiplication

The elliptic curves in class 171.d do not have complex multiplication.

Modular form 171.2.a.d

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