Properties

Label 417450l
Number of curves $1$
Conductor $417450$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 417450l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
417450.l1 417450l1 \([1, 1, 0, -84625, -10416875]\) \(-3222772836011/373770240\) \(-7773252960000000\) \([]\) \(3801600\) \(1.7854\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 417450l1 has rank \(1\).

Complex multiplication

The elliptic curves in class 417450l do not have complex multiplication.

Modular form 417450.2.a.l

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