Properties

Label 82800.s
Number of curves $1$
Conductor $82800$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 82800.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
82800.s1 82800fw1 \([0, 0, 0, -33375, -2267350]\) \(35248450000/1358127\) \(158411933280000\) \([]\) \(230400\) \(1.4924\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 82800.s1 has rank \(1\).

Complex multiplication

The elliptic curves in class 82800.s do not have complex multiplication.

Modular form 82800.2.a.s

sage: E.q_eigenform(10)
 
\(q - 3 q^{7} - 5 q^{11} + q^{13} + 4 q^{17} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display