Properties

Label 19600dc
Number of curves $1$
Conductor $19600$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("dc1")
 
E.isogeny_class()
 

Elliptic curves in class 19600dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19600.i1 19600dc1 \([0, 0, 0, 39200, 9089500]\) \(14155776/84035\) \(-39546534860000000\) \([]\) \(276480\) \(1.8666\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19600dc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 19600dc do not have complex multiplication.

Modular form 19600.2.a.dc

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} + 6 q^{9} + 5 q^{11} - 3 q^{13} - q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display