Properties

Label 21675m
Number of curves $1$
Conductor $21675$
CM no
Rank $1$

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

Elliptic curves in class 21675m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21675.r1 21675m1 \([1, 1, 0, -21825, 222750]\) \(35242105/19683\) \(642165563671875\) \([]\) \(68040\) \(1.5316\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21675m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 21675m do not have complex multiplication.

Modular form 21675.2.a.m

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