Properties

Label 47096.k
Number of curves $1$
Conductor $47096$
CM no
Rank $1$

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

Elliptic curves in class 47096.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.k1 47096f1 \([0, 1, 0, -280, -5264]\) \(-1682/7\) \(-10139580416\) \([]\) \(19680\) \(0.60514\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47096.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 47096.k do not have complex multiplication.

Modular form 47096.2.a.k

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