Properties

Label 17640.i
Number of curves $1$
Conductor $17640$
CM no
Rank $1$

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

Elliptic curves in class 17640.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17640.i1 17640r1 \([0, 0, 0, -3108, -1419068]\) \(-363080704/94921875\) \(-868020300000000\) \([]\) \(61440\) \(1.5457\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 17640.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 17640.i do not have complex multiplication.

Modular form 17640.2.a.i

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