Properties

Label 51800.a
Number of curves $1$
Conductor $51800$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 51800.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51800.a1 51800y1 \([0, 1, 0, -14208, -716912]\) \(-793036420/88837\) \(-35534800000000\) \([]\) \(122880\) \(1.3373\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51800.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 51800.a do not have complex multiplication.

Modular form 51800.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{7} + q^{9} + 2 q^{13} - 4 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display