Properties

Label 100010a
Number of curves $1$
Conductor $100010$
CM no
Rank $1$

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

Elliptic curves in class 100010a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100010.a1 100010a1 \([1, 1, 0, 147, -1763]\) \(347577210791/1638563840\) \(-1638563840\) \([]\) \(53760\) \(0.45044\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100010a1 has rank \(1\).

Complex multiplication

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

Modular form 100010.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 2 q^{7} - q^{8} - 2 q^{9} + q^{10} + 4 q^{11} - q^{12} + 2 q^{13} - 2 q^{14} + q^{15} + q^{16} + 7 q^{17} + 2 q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display