Properties

Label 1650i
Number of curves $1$
Conductor $1650$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 1650i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1650.f1 1650i1 \([1, 0, 1, -1, 8]\) \(-625/1188\) \(-29700\) \([]\) \(144\) \(-0.46279\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1650i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1650i do not have complex multiplication.

Modular form 1650.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - 3 q^{7} - q^{8} + q^{9} + q^{11} + q^{12} + 3 q^{14} + q^{16} - 5 q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display