Properties

Label 177744.c
Number of curves $1$
Conductor $177744$
CM no
Rank $2$

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

Elliptic curves in class 177744.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177744.c1 177744cv1 \([0, -1, 0, -44612, 2108496]\) \(489808/189\) \(3788998711835904\) \([]\) \(1059840\) \(1.6882\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177744.c1 has rank \(2\).

Complex multiplication

The elliptic curves in class 177744.c do not have complex multiplication.

Modular form 177744.2.a.c

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