Properties

Label 100510o
Number of curves $1$
Conductor $100510$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 100510o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100510.g1 100510o1 \([1, -1, 1, -25227, -1640421]\) \(-11993263569/972800\) \(-144009312819200\) \([]\) \(1020272\) \(1.4630\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100510o1 has rank \(0\).

Complex multiplication

The elliptic curves in class 100510o do not have complex multiplication.

Modular form 100510.2.a.o

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