Properties

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

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 61710cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61710.bv1 61710cd1 \([1, 1, 1, -513345, -145404225]\) \(-8444922396903721/253364474880\) \(-448850622482887680\) \([]\) \(1209600\) \(2.1652\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 61710cd1 has rank \(1\).

Complex multiplication

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

Modular form 61710.2.a.cd

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