Properties

Label 206310.e
Number of curves $1$
Conductor $206310$
CM no
Rank $1$

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

Elliptic curves in class 206310.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206310.e1 206310cn1 \([1, 1, 0, 7761742, -1622707788]\) \(349328659013909639/209872625664000\) \(-31068680716934455296000\) \([]\) \(22302720\) \(3.0051\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 206310.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 206310.e do not have complex multiplication.

Modular form 206310.2.a.e

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