Properties

Label 35322.k
Number of curves $1$
Conductor $35322$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 35322.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35322.k1 35322e1 \([1, 1, 0, -35339, 2558343]\) \(-8205738913/59682\) \(-35500245443922\) \([]\) \(181440\) \(1.4319\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 35322.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 35322.k do not have complex multiplication.

Modular form 35322.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - 2 q^{10} + 5 q^{11} - q^{12} + 3 q^{13} + q^{14} - 2 q^{15} + q^{16} - 6 q^{17} - q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display