Properties

Label 340032.er
Number of curves $1$
Conductor $340032$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("er1")
 
E.isogeny_class()
 

Elliptic curves in class 340032.er

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
340032.er1 340032er1 \([0, 1, 0, -833, -10209]\) \(-244140625/21252\) \(-5571084288\) \([]\) \(178176\) \(0.61426\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 340032.er1 has rank \(1\).

Complex multiplication

The elliptic curves in class 340032.er do not have complex multiplication.

Modular form 340032.2.a.er

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} - q^{11} + q^{13} + 5 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display