Properties

Label 72128z
Number of curves $1$
Conductor $72128$
CM no
Rank $1$

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

Elliptic curves in class 72128z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72128.b1 72128z1 \([0, 0, 0, -196, -2744]\) \(-6912/23\) \(-2770869248\) \([]\) \(55296\) \(0.49812\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 72128z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 72128z do not have complex multiplication.

Modular form 72128.2.a.z

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} - 2 q^{5} + 6 q^{9} - 2 q^{11} - 5 q^{13} + 6 q^{15} - 4 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display