Properties

Label 1638.m
Number of curves $1$
Conductor $1638$
CM no
Rank $1$

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

Elliptic curves in class 1638.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1638.m1 1638l1 \([1, -1, 1, -3749, 89437]\) \(-215773279370739/447469568\) \(-12081678336\) \([]\) \(1760\) \(0.82044\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1638.m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1638.m do not have complex multiplication.

Modular form 1638.2.a.m

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