Properties

Label 51600.c
Number of curves $1$
Conductor $51600$
CM no
Rank $1$

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

Elliptic curves in class 51600.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.c1 51600ck1 \([0, -1, 0, -192833, -35072088]\) \(-126879079874560/11907683883\) \(-74423024268750000\) \([]\) \(489600\) \(1.9794\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51600.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 51600.c do not have complex multiplication.

Modular form 51600.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4q^{7} + q^{9} - q^{11} - 5q^{13} - 6q^{17} + O(q^{20})\)  Toggle raw display