Properties

Label 409101be
Number of curves $1$
Conductor $409101$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 409101be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
409101.be1 409101be1 \([0, 1, 1, -2823, 57635]\) \(-4096000/69\) \(-41927534187\) \([]\) \(342720\) \(0.83716\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101be1 has rank \(1\).

Complex multiplication

The elliptic curves in class 409101be do not have complex multiplication.

Modular form 409101.2.a.be

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + q^{9} - 2 q^{12} - 4 q^{13} + 4 q^{16} - 2 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display