Properties

Label 33810.p
Number of curves $1$
Conductor $33810$
CM no
Rank $2$

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

Elliptic curves in class 33810.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33810.p1 33810o1 \([1, 1, 0, -1397, 19881]\) \(-125720594041/2587500\) \(-6212587500\) \([]\) \(39360\) \(0.67063\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 33810.p1 has rank \(2\).

Complex multiplication

The elliptic curves in class 33810.p do not have complex multiplication.

Modular form 33810.2.a.p

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