Properties

Label 289578.c
Number of curves $1$
Conductor $289578$
CM no
Rank $0$

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

Elliptic curves in class 289578.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
289578.c1 289578c1 \([1, 0, 1, 162845, 8056862]\) \(19785968032823/12608077824\) \(-304328348434169856\) \([]\) \(5723136\) \(2.0437\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 289578.c1 has rank \(0\).

Complex multiplication

The elliptic curves in class 289578.c do not have complex multiplication.

Modular form 289578.2.a.c

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