Properties

Label 32192.i
Number of curves $1$
Conductor $32192$
CM no
Rank $1$

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

Elliptic curves in class 32192.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32192.i1 32192bb1 \([0, -1, 0, 7, -71]\) \(8000/503\) \(-2060288\) \([]\) \(3072\) \(-0.10886\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 32192.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 32192.i do not have complex multiplication.

Modular form 32192.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} + 3 q^{7} - 2 q^{9} + 3 q^{11} + q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display