Properties

Label 1740.g
Number of curves $1$
Conductor $1740$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 1740.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1740.g1 1740h1 \([0, 1, 0, -190, 1025]\) \(-47659369216/4404375\) \(-70470000\) \([]\) \(480\) \(0.24839\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1740.g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1740.g do not have complex multiplication.

Modular form 1740.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 3 q^{7} + q^{9} - 3 q^{11} + q^{13} + q^{15} - 3 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display