Properties

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

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

Elliptic curves in class 19600c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19600.bg1 19600c1 \([0, -1, 0, -408, -2813]\) \(12544\) \(600250000\) \([]\) \(6720\) \(0.42785\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19600c1 has rank \(1\).

Complex multiplication

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

Modular form 19600.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{9} - 3 q^{11} + 6 q^{13} + 5 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display