Properties

Label 2205m
Number of curves $1$
Conductor $2205$
CM no
Rank $0$

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

Elliptic curves in class 2205m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2205.m1 2205m1 \([0, 0, 1, -136857, 32113975]\) \(-1376628736/1366875\) \(-281472991507141875\) \([]\) \(37632\) \(2.0440\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2205m1 has rank \(0\).

Complex multiplication

The elliptic curves in class 2205m do not have complex multiplication.

Modular form 2205.2.a.m

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