Properties

Label 77658be
Number of curves $1$
Conductor $77658$
CM no
Rank $1$

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

Elliptic curves in class 77658be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77658.bg1 77658be1 \([1, 0, 0, -9821, 372579]\) \(1317614126347/4941258\) \(392864599806\) \([]\) \(133056\) \(1.0842\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77658be1 has rank \(1\).

Complex multiplication

The elliptic curves in class 77658be do not have complex multiplication.

Modular form 77658.2.a.be

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