Properties

Label 605.a
Number of curves $1$
Conductor $605$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 605.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
605.a1 605c1 [1, -1, 1, -12, 36] [] 120 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 605.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 605.a do not have complex multiplication.

Modular form 605.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{2} - 3q^{3} - q^{4} + q^{5} + 3q^{6} - 3q^{7} + 3q^{8} + 6q^{9} - q^{10} + 3q^{12} + 4q^{13} + 3q^{14} - 3q^{15} - q^{16} - 6q^{18} + 4q^{19} + O(q^{20}) \)