Properties

Label 364650.f
Number of curves $1$
Conductor $364650$
CM no
Rank $2$

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

Elliptic curves in class 364650.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.f1 364650f1 \([1, 1, 0, 404800, 104544000]\) \(18779477838616535/22915878365952\) \(-8951514986700000000\) \([]\) \(9400320\) \(2.3227\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 364650.f1 has rank \(2\).

Complex multiplication

The elliptic curves in class 364650.f do not have complex multiplication.

Modular form 364650.2.a.f

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