Properties

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

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 77658.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77658.c1 77658c1 \([1, 1, 0, 763599, 404326269]\) \(4212803783/8470728\) \(-99007565361082563528\) \([]\) \(2600640\) \(2.5213\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77658.c1 has rank \(1\).

Complex multiplication

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

Modular form 77658.2.a.c

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