Properties

Label 2205.j
Number of curves $1$
Conductor $2205$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2205.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2205.j1 2205h1 \([0, 0, 1, -63, -331]\) \(-110592/125\) \(-31255875\) \([]\) \(672\) \(0.13255\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2205.j1 has rank \(1\).

Complex multiplication

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

Modular form 2205.2.a.j

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