Properties

Label 409101.c
Number of curves $1$
Conductor $409101$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 409101.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
409101.c1 409101c1 \([0, -1, 1, 2156180, -102986346]\) \(5319051554816/3099832659\) \(-646074500666393526651\) \([]\) \(27648000\) \(2.6826\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101.c1 has rank \(2\).

Complex multiplication

The elliptic curves in class 409101.c do not have complex multiplication.

Modular form 409101.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + q^{9} - 2 q^{10} - 2 q^{12} + 6 q^{13} - q^{15} - 4 q^{16} - 2 q^{17} - 2 q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display