Properties

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

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 51800r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51800.x1 51800r1 \([0, -1, 0, -15008, 716012]\) \(-11683450802/63455\) \(-2030560000000\) \([]\) \(135936\) \(1.2055\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51800r1 has rank \(0\).

Complex multiplication

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

Modular form 51800.2.a.r

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{7} + q^{9} + 6 q^{11} + 3 q^{13} - 8 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display