Properties

Label 130130.o
Number of curves $1$
Conductor $130130$
CM no
Rank $1$

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

Elliptic curves in class 130130.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
130130.o1 130130o1 \([1, 1, 0, -408138, -105930482]\) \(-9217213605769/589531250\) \(-480898751614531250\) \([]\) \(2149056\) \(2.1462\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 130130.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 130130.o do not have complex multiplication.

Modular form 130130.2.a.o

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