Properties

Label 135240bz
Number of curves $1$
Conductor $135240$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 135240bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
135240.r1 135240bz1 \([0, -1, 0, -16, 1]\) \(614656/345\) \(270480\) \([]\) \(21120\) \(-0.26751\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 135240bz1 has rank \(1\).

Complex multiplication

The elliptic curves in class 135240bz do not have complex multiplication.

Modular form 135240.2.a.bz

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} + 5 q^{11} + 2 q^{13} + q^{15} - 8 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display