Properties

Label 348726cf
Number of curves $1$
Conductor $348726$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cf1")
 
E.isogeny_class()
 

Elliptic curves in class 348726cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348726.cf1 348726cf1 \([1, 1, 1, -2715, -59847]\) \(-16983563041/1599696\) \(-208473982416\) \([]\) \(490752\) \(0.91388\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 348726cf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 348726cf do not have complex multiplication.

Modular form 348726.2.a.cf

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + q^{10} + 5 q^{11} - q^{12} + 4 q^{13} - q^{14} - q^{15} + q^{16} + 3 q^{17} + q^{18} + O(q^{20})\) Copy content Toggle raw display