Properties

Label 35234.e
Number of curves $1$
Conductor $35234$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 35234.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35234.e1 35234e1 \([1, 1, 1, -312, -2243]\) \(3359498792833/15714364\) \(15714364\) \([]\) \(15456\) \(0.23080\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 35234.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 35234.e do not have complex multiplication.

Modular form 35234.2.a.e

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