Properties

Label 179776b
Number of curves $1$
Conductor $179776$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 179776b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
179776.c1 179776b1 \([0, 1, 0, -58161281, 539979415423]\) \(-25153757/131072\) \(-113379013690573239504338944\) \([]\) \(53973504\) \(3.6836\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 179776b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 179776b do not have complex multiplication.

Modular form 179776.2.a.b

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