Properties

Label 142.d
Number of curves $1$
Conductor $142$
CM no
Rank $1$

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

Elliptic curves in class 142.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
142.d1 142a1 \([1, -1, 1, -12, 15]\) \(176558481/36352\) \(36352\) \([]\) \(36\) \(-0.40960\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 142.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 142.d do not have complex multiplication.

Modular form 142.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} - 4 q^{5} - 3 q^{6} - 3 q^{7} + q^{8} + 6 q^{9} - 4 q^{10} - 3 q^{12} + q^{13} - 3 q^{14} + 12 q^{15} + q^{16} + 6 q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display