Properties

Label 223756.d
Number of curves $1$
Conductor $223756$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 223756.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
223756.d1 223756d1 \([0, 1, 0, 451, 6904]\) \(131072/331\) \(-25562780464\) \([]\) \(207360\) \(0.68083\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 223756.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 223756.d do not have complex multiplication.

Modular form 223756.2.a.d

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