Properties

Label 461719.a
Number of curves $1$
Conductor $461719$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 461719.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
461719.a1 461719a1 \([1, 1, 0, -15891, -779410]\) \(-9434056897/24301\) \(-1143261954181\) \([]\) \(1290240\) \(1.1899\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 461719.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 461719.a do not have complex multiplication.

Modular form 461719.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} - q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} + q^{9} - 2 q^{10} - 5 q^{11} - 2 q^{12} + q^{13} - 4 q^{14} - 4 q^{15} - q^{16} - 7 q^{17} + q^{18} + O(q^{20})\) Copy content Toggle raw display