Properties

Label 163254.a
Number of curves $1$
Conductor $163254$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 163254.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
163254.a1 163254ct1 \([1, 1, 0, -94830414, -355482197676]\) \(558058791583853833465367617/9081241477824096\) \(1534729809752272224\) \([]\) \(19152000\) \(3.0345\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 163254.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 163254.a do not have complex multiplication.

Modular form 163254.2.a.a

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