Properties

Label 101a
Number of curves $1$
Conductor $101$
CM no
Rank $1$

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

Elliptic curves in class 101a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101.a1 101a1 \([0, 1, 1, -1, -1]\) \(262144/101\) \(101\) \([]\) \(2\) \(-0.91636\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 101a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 101a do not have complex multiplication.

Modular form 101.2.a.a

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