Properties

Label 40768p
Number of curves $1$
Conductor $40768$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 40768p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40768.cv1 40768p1 \([0, 1, 0, -3201, 71903]\) \(-235298/13\) \(-200466366464\) \([]\) \(29952\) \(0.92650\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40768p1 has rank \(0\).

Complex multiplication

The elliptic curves in class 40768p do not have complex multiplication.

Modular form 40768.2.a.p

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