Properties

Label 223767m
Number of curves $1$
Conductor $223767$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 223767m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
223767.n1 223767m1 \([0, 0, 1, -58719, 2077515]\) \(207474688/102789\) \(11092800064932909\) \([]\) \(2439360\) \(1.7718\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 223767m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 223767m do not have complex multiplication.

Modular form 223767.2.a.m

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} - 3 q^{5} + 3 q^{7} - 6 q^{10} - 5 q^{11} + 2 q^{13} + 6 q^{14} - 4 q^{16} - 6 q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display