Properties

Label 61710r
Number of curves $1$
Conductor $61710$
CM no
Rank $0$

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

Elliptic curves in class 61710r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61710.p1 61710r1 \([1, 1, 0, 3023, 72109]\) \(14245319/18360\) \(-3935629055160\) \([]\) \(171072\) \(1.1027\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 61710r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 61710r do not have complex multiplication.

Modular form 61710.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - q^{10} - q^{12} - q^{13} - q^{14} - q^{15} + q^{16} + q^{17} - q^{18} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display