Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 56550.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.p1 56550g1 \([1, 1, 0, 21875, -1953125]\) \(74082708125999/149327343750\) \(-2333239746093750\) \([]\) \(359424\) \(1.6333\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 56550.p1 has rank \(0\).

Complex multiplication

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

Modular form 56550.2.a.p

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