Properties

Label 344760.bg
Number of curves $1$
Conductor $344760$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 344760.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
344760.bg1 344760bg1 \([0, -1, 0, 1291780, -2792217975]\) \(3086803246205696/45384521484375\) \(-3504998668183593750000\) \([]\) \(18869760\) \(2.8147\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 344760.bg1 has rank \(1\).

Complex multiplication

The elliptic curves in class 344760.bg do not have complex multiplication.

Modular form 344760.2.a.bg

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 3 q^{7} + q^{9} - 3 q^{11} - q^{15} - q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display