Properties

Label 203840.ef
Number of curves $1$
Conductor $203840$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ef1")
 
E.isogeny_class()
 

Elliptic curves in class 203840.ef

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
203840.ef1 203840cf1 \([0, 1, 0, -4589601, 3969890399]\) \(-693346671296498/40610171875\) \(-626228738250752000000\) \([]\) \(9584640\) \(2.7465\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 203840.ef1 has rank \(1\).

Complex multiplication

The elliptic curves in class 203840.ef do not have complex multiplication.

Modular form 203840.2.a.ef

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