Properties

Label 333270.ce
Number of curves $1$
Conductor $333270$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 333270.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.ce1 333270ce1 \([1, -1, 0, -46919754, 125275968580]\) \(-200097047358049/2940552720\) \(-167872356384190970939280\) \([]\) \(54405120\) \(3.2605\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 333270.ce1 has rank \(1\).

Complex multiplication

The elliptic curves in class 333270.ce do not have complex multiplication.

Modular form 333270.2.a.ce

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