Properties

Label 324723.a
Number of curves $1$
Conductor $324723$
CM no
Rank $1$

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

Elliptic curves in class 324723.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
324723.a1 324723a1 \([0, -1, 1, -1334972, 225653420]\) \(207474688/102789\) \(130353299553081702069\) \([]\) \(20401920\) \(2.5528\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 324723.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 324723.a do not have complex multiplication.

Modular form 324723.2.a.a

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