Properties

Label 222180.m
Number of curves $1$
Conductor $222180$
CM no
Rank $1$

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

Elliptic curves in class 222180.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
222180.m1 222180k1 \([0, 1, 0, -129781, 14840135]\) \(12058624/2205\) \(44204984971418880\) \([]\) \(1695744\) \(1.9126\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 222180.m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 222180.m do not have complex multiplication.

Modular form 222180.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} - 3 q^{11} + 2 q^{13} - q^{15} - 4 q^{17} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display