Properties

Label 33635m
Number of curves $1$
Conductor $33635$
CM no
Rank $1$

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

Elliptic curves in class 33635m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33635.o1 33635m1 \([0, 1, 1, -320, 262771]\) \(-4096/33635\) \(-29851186310435\) \([]\) \(122880\) \(1.2645\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 33635m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 33635m do not have complex multiplication.

Modular form 33635.2.a.m

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