Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.k1 51600d1 \([0, -1, 0, -3, -18]\) \(-10240/387\) \(-154800\) \([]\) \(6528\) \(-0.32398\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51600.k1 has rank \(1\).

Complex multiplication

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

Modular form 51600.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{7} + q^{9} - q^{11} + 5q^{13} - 6q^{17} + 6q^{19} + O(q^{20})\)  Toggle raw display