Properties

Label 135240.s
Number of curves $1$
Conductor $135240$
CM no
Rank $1$

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

Elliptic curves in class 135240.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
135240.s1 135240cb1 \([0, -1, 0, 229, -804]\) \(34420736/25875\) \(-994014000\) \([]\) \(67968\) \(0.41462\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 135240.s1 has rank \(1\).

Complex multiplication

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

Modular form 135240.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} + 6 q^{11} + q^{15} - q^{17} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display