Properties

Label 61710d
Number of curves $1$
Conductor $61710$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 61710d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61710.d1 61710d1 \([1, 1, 0, -10408, -17652092]\) \(-70393838689/75905555220\) \(-134471321311098420\) \([]\) \(672000\) \(1.9657\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 61710d1 has rank \(1\).

Complex multiplication

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

Modular form 61710.2.a.d

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