Properties

Label 21858a
Number of curves $1$
Conductor $21858$
CM no
Rank $3$

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

Elliptic curves in class 21858a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21858.a1 21858a1 \([1, 1, 0, -32, 60]\) \(-3803721481/131148\) \(-131148\) \([]\) \(9984\) \(-0.24473\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21858a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 21858a do not have complex multiplication.

Modular form 21858.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 4 q^{5} + q^{6} - 5 q^{7} - q^{8} + q^{9} + 4 q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 5 q^{14} + 4 q^{15} + q^{16} - 6 q^{17} - q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display