Properties

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

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 82800.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
82800.z1 82800di1 \([0, 0, 0, -7786875, 5313006250]\) \(1790712239425/618098688\) \(18023757742080000000000\) \([]\) \(4423680\) \(2.9723\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 82800.z1 has rank \(1\).

Complex multiplication

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

Modular form 82800.2.a.z

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