Properties

Label 40950.et
Number of curves $1$
Conductor $40950$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("et1")
 
E.isogeny_class()
 

Elliptic curves in class 40950.et

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40950.et1 40950ek1 \([1, -1, 1, -22608905, 41620153097]\) \(-112205650221491190337/745029571313664\) \(-8486352460744704000000\) \([]\) \(4112640\) \(3.0433\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40950.et1 has rank \(1\).

Complex multiplication

The elliptic curves in class 40950.et do not have complex multiplication.

Modular form 40950.2.a.et

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} - q^{11} + q^{13} + q^{14} + q^{16} + 7 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display