Properties

Label 100800pz
Number of curves $1$
Conductor $100800$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("pz1")
 
E.isogeny_class()
 

Elliptic curves in class 100800pz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.po1 100800pz1 \([0, 0, 0, -4500, 135000]\) \(-34560/7\) \(-2041200000000\) \([]\) \(184320\) \(1.0845\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100800pz1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100800pz do not have complex multiplication.

Modular form 100800.2.a.pz

sage: E.q_eigenform(10)
 
\(q + q^{7} + 5 q^{11} - 6 q^{13} + 4 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display