Properties

Label 56550.o
Number of curves $1$
Conductor $56550$
CM no
Rank $0$

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

Elliptic curves in class 56550.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.o1 56550f1 \([1, 1, 0, -415, -10235]\) \(-317367253345/1565810688\) \(-39145267200\) \([]\) \(50544\) \(0.71700\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 56550.o1 has rank \(0\).

Complex multiplication

The elliptic curves in class 56550.o do not have complex multiplication.

Modular form 56550.2.a.o

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