Properties

Label 49098.be
Number of curves $1$
Conductor $49098$
CM no
Rank $1$

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

Elliptic curves in class 49098.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49098.be1 49098bd1 \([1, 1, 1, -29, 83]\) \(-55164193/48096\) \(-2356704\) \([]\) \(12480\) \(-0.079968\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 49098.be1 has rank \(1\).

Complex multiplication

The elliptic curves in class 49098.be do not have complex multiplication.

Modular form 49098.2.a.be

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