Properties

Label 494.c
Number of curves $1$
Conductor $494$
CM no
Rank $0$

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

Elliptic curves in class 494.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
494.c1 494c1 \([1, -1, 0, -61, -169]\) \(-25334470953/9386\) \(-9386\) \([]\) \(152\) \(-0.27024\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 494.c1 has rank \(0\).

Complex multiplication

The elliptic curves in class 494.c do not have complex multiplication.

Modular form 494.2.a.c

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