Properties

Label 858.e
Number of curves $1$
Conductor $858$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 858.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
858.e1 858f1 \([1, 1, 1, -572, 118685]\) \(-20699471212993/6097712265216\) \(-6097712265216\) \([]\) \(2640\) \(1.1324\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 858.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 858.e do not have complex multiplication.

Modular form 858.2.a.e

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