Properties

Label 100010.d
Number of curves $1$
Conductor $100010$
CM no
Rank $1$

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

Elliptic curves in class 100010.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100010.d1 100010d1 \([1, 1, 0, 3, -169]\) \(1685159/12501250\) \(-12501250\) \([]\) \(27136\) \(0.040694\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100010.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100010.d do not have complex multiplication.

Modular form 100010.2.a.d

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