Properties

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

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 61710m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61710.l1 61710m1 \([1, 1, 0, -552, 4866]\) \(-14014952531/318750\) \(-424256250\) \([]\) \(27840\) \(0.44334\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 61710m1 has rank \(1\).

Complex multiplication

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

Modular form 61710.2.a.m

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