Properties

Label 213444.w
Number of curves $1$
Conductor $213444$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 213444.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
213444.w1 213444s1 \([0, 0, 0, 6972504, 1521167956]\) \(401408/243\) \(-22693959648478265672448\) \([]\) \(14112000\) \(2.9789\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 213444.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 213444.w do not have complex multiplication.

Modular form 213444.2.a.w

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 3 q^{13} - 8 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display