Properties

Label 58870t
Number of curves $1$
Conductor $58870$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 58870t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58870.v1 58870t1 \([1, 1, 1, -14735, 8279035]\) \(-841/70\) \(-29449506331014070\) \([]\) \(487200\) \(1.8398\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 58870t1 has rank \(1\).

Complex multiplication

The elliptic curves in class 58870t do not have complex multiplication.

Modular form 58870.2.a.t

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