Properties

Label 51842.o
Number of curves $1$
Conductor $51842$
CM no
Rank $0$

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

Elliptic curves in class 51842.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51842.o1 51842m1 \([1, 0, 0, 1714, -12412]\) \(8947391/6272\) \(-390346205312\) \([]\) \(96768\) \(0.91270\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51842.o1 has rank \(0\).

Complex multiplication

The elliptic curves in class 51842.o do not have complex multiplication.

Modular form 51842.2.a.o

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