Properties

Label 1710.r
Number of curves $1$
Conductor $1710$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 1710.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1710.r1 1710q1 \([1, -1, 1, 13, -39]\) \(357911/950\) \(-692550\) \([]\) \(240\) \(-0.19566\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1710.r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 1710.r do not have complex multiplication.

Modular form 1710.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} - 3 q^{13} - q^{14} + q^{16} + 7 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display