Properties

Label 77658.o
Number of curves $1$
Conductor $77658$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 77658.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77658.o1 77658u1 \([1, 0, 1, -3077390585, -39130754228068]\) \(509871621645082002682657/190423143557704974336\) \(1203733823360098624011083710464\) \([]\) \(176964480\) \(4.4717\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77658.o1 has rank \(0\).

Complex multiplication

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

Modular form 77658.2.a.o

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