Properties

Label 348726.e
Number of curves $1$
Conductor $348726$
CM no
Rank $1$

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

Elliptic curves in class 348726.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348726.e1 348726e1 \([1, 1, 0, -3188720, -1843114752]\) \(211127242011625/35895508992\) \(609633639854414364672\) \([]\) \(18604800\) \(2.7089\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 348726.e1 has rank \(1\).

Complex multiplication

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

Modular form 348726.2.a.e

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