Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 32192.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32192.s1 32192a1 \([0, 1, 0, 47, 79]\) \(686000/503\) \(-8241152\) \([]\) \(6144\) \(0.015350\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 32192.s1 has rank \(1\).

Complex multiplication

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

Modular form 32192.2.a.s

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