Properties

Label 3330.f
Number of curves $1$
Conductor $3330$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3330.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3330.f1 3330j1 \([1, -1, 0, -2529, -63747]\) \(-2454365649169/1035763200\) \(-755071372800\) \([]\) \(8064\) \(0.98701\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3330.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3330.f do not have complex multiplication.

Modular form 3330.2.a.f

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