Properties

Label 47096i
Number of curves $1$
Conductor $47096$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47096i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.e1 47096i1 \([0, -1, 0, 154464, -1397376788]\) \(397822/823543\) \(-843723636058400405504\) \([]\) \(1851360\) \(2.6943\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47096i1 has rank \(1\).

Complex multiplication

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

Modular form 47096.2.a.i

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