Properties

Label 242760.w
Number of curves $1$
Conductor $242760$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 242760.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
242760.w1 242760w1 \([0, -1, 0, -219056, 40040700]\) \(-3928197859398724/58604765625\) \(-17343259920000000\) \([]\) \(2032128\) \(1.9195\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 242760.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 242760.w do not have complex multiplication.

Modular form 242760.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + 3 q^{11} + 3 q^{13} + q^{15} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display