Properties

Label 3234.a
Number of curves $1$
Conductor $3234$
CM no
Rank $0$

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

Elliptic curves in class 3234.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3234.a1 3234e1 \([1, 1, 0, -4869, -137619]\) \(-260607143968297/11270993184\) \(-552278666016\) \([]\) \(8400\) \(1.0188\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3234.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 3234.a do not have complex multiplication.

Modular form 3234.2.a.a

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