Properties

Label 2576o
Number of curves $1$
Conductor $2576$
CM no
Rank $1$

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

Elliptic curves in class 2576o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2576.g1 2576o1 \([0, -1, 0, 6, 43]\) \(1257728/55223\) \(-883568\) \([]\) \(192\) \(-0.17923\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2576o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2576o do not have complex multiplication.

Modular form 2576.2.a.o

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