Properties

Label 100007a
Number of curves $1$
Conductor $100007$
CM no
Rank $0$

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

Elliptic curves in class 100007a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100007.a1 100007a1 \([1, -1, 0, -121, 544]\) \(-196832673513/100007\) \(-100007\) \([]\) \(34592\) \(-0.088606\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100007a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 100007a do not have complex multiplication.

Modular form 100007.2.a.a

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