Properties

Label 414050.ds
Number of curves $1$
Conductor $414050$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ds1")
 
E.isogeny_class()
 

Elliptic curves in class 414050.ds

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
414050.ds1 414050ds1 \([1, -1, 0, -1487992, -754965184]\) \(-1026590625/100352\) \(-35616759488011520000\) \([]\) \(24330240\) \(2.4925\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 414050.ds1 has rank \(1\).

Complex multiplication

The elliptic curves in class 414050.ds do not have complex multiplication.

Modular form 414050.2.a.ds

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