Properties

Label 77658.e
Number of curves $1$
Conductor $77658$
CM no
Rank $1$

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

Elliptic curves in class 77658.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77658.e1 77658m1 \([1, 1, 0, -1780625, -1732344849]\) \(-28890625/43218\) \(-934005042615518673282\) \([]\) \(4045440\) \(2.7156\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77658.e1 has rank \(1\).

Complex multiplication

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

Modular form 77658.2.a.e

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