Properties

Label 58621.d
Number of curves $1$
Conductor $58621$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 58621.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58621.d1 58621d1 \([1, 1, 1, -1942, -35600]\) \(-912673/61\) \(-54137724541\) \([]\) \(61440\) \(0.81153\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 58621.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 58621.d do not have complex multiplication.

Modular form 58621.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} - q^{4} - 3 q^{5} - 2 q^{6} + q^{7} + 3 q^{8} + q^{9} + 3 q^{10} + 5 q^{11} - 2 q^{12} - q^{13} - q^{14} - 6 q^{15} - q^{16} - 4 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display