Properties

Label 262558.c
Number of curves $1$
Conductor $262558$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 262558.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
262558.c1 262558c1 \([1, -1, 1, -4855821, -4100350923]\) \(2003092024307193/9529458688\) \(60239168027295219712\) \([]\) \(26331480\) \(2.6446\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 262558.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 262558.c do not have complex multiplication.

Modular form 262558.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} - 2 q^{5} - 3 q^{6} + 3 q^{7} + q^{8} + 6 q^{9} - 2 q^{10} - 6 q^{11} - 3 q^{12} - 5 q^{13} + 3 q^{14} + 6 q^{15} + q^{16} + 6 q^{17} + 6 q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display