Properties

Label 54777c
Number of curves $1$
Conductor $54777$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 54777c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54777.b1 54777c1 \([0, 1, 1, -2242, -45710]\) \(-1404928/171\) \(-151763129451\) \([]\) \(118560\) \(0.88045\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 54777c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 54777c do not have complex multiplication.

Modular form 54777.2.a.c

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