Properties

Label 57498u
Number of curves $1$
Conductor $57498$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 57498u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57498.v1 57498u1 \([1, 0, 0, 62261, 118860401]\) \(7599023/1741824\) \(-6118121012346491904\) \([]\) \(1864800\) \(2.2840\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 57498u1 has rank \(0\).

Complex multiplication

The elliptic curves in class 57498u do not have complex multiplication.

Modular form 57498.2.a.u

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