Properties

Label 47775.k
Number of curves $1$
Conductor $47775$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 47775.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47775.k1 47775dc1 \([0, 1, 1, 572, 6304]\) \(28672/39\) \(-28103404875\) \([]\) \(46368\) \(0.69067\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47775.k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 47775.k do not have complex multiplication.

Modular form 47775.2.a.k

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